Q2 of 108 Page 36

Find a quadratic polynomial the sum and the product of whose zeroes are respectively the given numbers.

–3, 2


Let the two zeroes be a and b.

The generalized form of the quadratic equation with sum and product of zeroes a and b is as follows:


ax2 + bx + c = 0 ………………… (i)


Now in this case


∴ a + b = -b/a = -3


∴ ab = c / a = 2


If a = k where k is any real number


b = 3k ………………… (ii)


c = 2k ………………… (iii)


Put values from (ii) and (iii) in (i)


kx2 + 3kx + 2k = 0


k (x2 + 3x + 2) = 0


Therefore the quadratic equation is as follows:


x2 + 3x + 2 = 0


More from this chapter

All 108 →
1

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.


1

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

3x2 – x – 4


 2

Find a quadratic polynomial the sum and the product of whose zeroes are respectively the given numbers.


 2

Find a quadratic polynomial the sum and the product of whose zeroes are respectively the given numbers.