Age of first friend = (x – 4) yrs . and age of second friend = (20 – x – 4) yrs = (16 – x) yrs. So, the given quadratic equation has no real roots and hence it is not possible to calculate the present ages.
Is the following situation possible the sum of ages of a mother and daughter is 25 years?
Answer Expert Verified
Here, Discriminant D is less than 0, So No real value is possible, Hence this situation is not possible .
When the present age of the mother is added to the present age of the daughter the sum is 40 years what will be their total age after 5 years?
Now, we are given that the mother’s age will be twice her daughter’s age . Hence, the present age of the mother is 40 years and the present age of the daughter is 10 years.
Is it possible to design a rectangle of perimeter 100m and area 400m2?
Yes , it is possible to design a rectangular park of perimeter 80 m and area 400 m 2 . The length and breadth both are equal to 40 m. Hence, the park will be square in shape.
Can you design a rectangular park of perimeter 80 m and area 400 m2?
Yes, it is possible . Hence, breadth of the rectangular park be 20 meters and length be 20 meters.
What do you observe about the sum and the product of the roots of each quadratic equation?
The sum of the roots of a quadratic equation is equal to the negation of the coefficient of the second term, divided by the leading coefficient . The product of the roots of a quadratic equation is equal to the constant term (the third term), divided by the leading coefficient.
When the present age of mother is added to the present age of daughter?
When the present age of mother is added to the present age of daughter, the total is 40 years .
Can you design a rectangular park of perimeter 80m and area 300 m2?
yes it is possible ...to draw a rectangle of length 30 m and breadth 10m.
Is it possible to design a rectangular plot?
Let length of the rectangular park be x m and breadth be y m. So, the given quadratic equation has equal roots and hence it is possible to design a rectangular park.
Is it possible to design a rectangular rice field whose length is twice its width and the area is 800m 2?
no its is not possible .
Do you think a quadratic equation can be determined given the sum and product of its roots?
If a quadratic equation is given in standard form, we can find the sum and product of the roots using coefficient of x 2 , x and constant term .
Does there exist a quadratic equation whose coefficients are all distinct Irrationals?
Yes , consider the quadratic equation with all distinct irrationals coefficients i.e., √3×2 – 7 √3x + 12√3 = 0. The roots of this quadratic equation are 3 and 4, which are rationals.
Is it possible to design a rectangular rice field?
no its is not possible .
What do you observe about the relationship between the number of roots and the degree of polynomials?
Remember that the degree of a polynomial, the highest exponent, dictates the maximum number of roots it can have. Thus, the degree of a polynomial with a given number of roots is equal to or greater than the number of roots that are given .
Which one of the following is a quadratic equation?
In math, we define a quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is y = ax^2 + bx + c , where a, b, and c are numbers and a cannot be 0. Examples of quadratic equations include all of these: y = x^2 + 3x + 1.
Which of the following is a root of the equation 2×2 5x 3 0?
Hence, 3/2 and 1 are the roots of the equation.
Can a quadratic equation ax2 bx 0 has non real roots?
No because , Here the value of c = 0.
Is every quadratic equation has two real roots?
A quadratic equation has exactly two roots , no more no less. A quadratic equation can’t have more than two roots. So, if coefficient of x 2 (a) and constant term(c) have the same sign and coefficient of x(b) is zero, then the roots will be imaginary.
Is it possible that the sum of ages of two boys is 20 years and 4 years ago the product of their ages was 48 years?
Sum of age of two friends is 20 years. Hence, It is not possible to find the present age .
Is it possible to design a rectangular mango grove whose length is twice its breadth and area is 800m2?
Summary: It is possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2 with length and breadth as 40 m and 20 m respectively.
What is the meaning of mango Grove?
mango grove means mango trees planted in such numbers that they preclude or when full grown .
Does there exist a quadratic equation whose coefficients are all distinct Irrationals but both the roots are rational justify your answer?
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify you answer. Yes , consider the quadratic equation 2×2+x-4=0 with rational coefficient. The roots of the given quadratic equation are -1+√334 and -1-√334 are irrational.
Does a quadratic equation with integral coefficients has integral roots justify your answer?
No, a quadratic equation with integral coefficients may or may not have integral roots . The roots of the given equation are 1⁄2 and – 1⁄4 which are not integers. Hence, a quadratic equation with integral coefficient might or might not have integral roots.
Can both the roots of quadratic equation be zero?
Roots are also called x-intercepts or zeros. A quadratic function is graphically represented by a parabola with vertex located at the origin, below the x-axis, or above the x-axis. Therefore, a quadratic function may have one, two, or zero roots.
