Question

2. If a and B are two distinct zeros of a quadratic polynomial such that
a - B = 3 and aß = 4 then the polynomial is
()x2 + 5x – 4(ii) - x2 + 5x + 4(iii)x2 + 5x + 4 (iv) None of these​

Answer 1

GIVEN :–

• α - β = 3

• αβ = 4

TO FIND :–

• quadratic equation = ?

SOLUTION :–

• Let –

=> α - β = 3

=> α = 3 + β ———————eq.(1)

• And –

=> αβ = 4 ———————eq.(2)

• Put the value of 'α' from eq.(1) in eq.(2) –

=> (3 + β)β = 4

=> β² + 3β - 4 = 0

=> β² + 4β - β - 4 = 0

=> β(β + 4) -(β + 4) =0

=> (β - 1)(β + 4) = 0

=> β = 1 , -4

• And –

=> α = 4 , -1

● When α = 4 & β = 1 :–

▪︎ quadratic equation –

=> x² - (α + β) x + αβ = 0

=> x² - (4 + 1) x + (4)(1) = 0

=> x² - 5x + 4 = 0

● When α = -1 & β = -4 :–

▪︎ quadratic equation –

=> x² - (α + β) x + αβ = 0

=> x² - (-4 - 1) x + (-4)(-1) = 0

=> x² + 5x + 4 = 0

● Hence , Option (iii) is correct.