Question

Find the quadratic polynomial having zeroes 5 and 3.

Answer 1

GIVEN :–

• Zero's of quadratic equation is 5 and 3.

TO FIND :–

• Quadratic equation = ?

SOLUTION :–

• We know that quadratic equation –

=> x² - ( Sum of roots ) x + Product of roots = 0

• Now Let's find –

=> Sum of roots = 5 + 3

=> Sum of roots = 8

• Product of roots = (5)(3)

=> Product of roots = 15

• Now put the values –

=> x² - 8x + 15 = 0

VERIFICATION :–

• We know that –

=> Sum of roots = -( coffieciant of x)/(coffieciant of x²)

=> 5 + 3 = -(-8)/1

=> 8 = 8 (verified)

• And –

=> Product of roots = (constant term)/(coffieciant of x²)

=> (5)(3) = 15/1

=> 15 = 15 (verified)

Answer 2

Let α & β be zeros of quadratic polynomial.

➫ Let α=5 and β=3

Quadratic polynomial :-

x² - (Sum of zeros) + (Product of zeros) =0

↦ x² - (α+β)x + αβ = 0

↦ x² - (5+3)x + 5×3 = 0

↦ x² - 8x + 15 = 0

➫ The quadratic polynomial is-

x² - 8x + 15 = 0