Question

Find the quadratic equation whose roots are 1 and 3/2

Answer 1

ANSWER:

• Required polynomial is :

$= \dfrac{1}{2} (2x {}^{2} - 5x + 3)$

GIVEN:

• Zeros of the Quadratic polynomial are 1 and 3/2

TO FIND:

• Quadratic polynomial

SOLUTION:

Quadratic polynomial when Zeros are given:

= x²-(α+β)x+αβ

Finding sum of zeros (α+β)

$= 1 + \dfrac{3}{2} \\ \\ = \dfrac{2 + 3}{2} \\ \\ = \dfrac{5}{2}$

Finding product of zeros (αβ)

$= \dfrac{3}{2} \times 1 \\ \\ = \dfrac{3}{2}$

Quadratic polynomial :

$= x {}^{2} - \dfrac{5}{2} x + \dfrac{3}{2} \\ \\ = \dfrac{1}{2} (2x {}^{2} - 5x + 3)$