Question

If alpha and bita are zeros of quadratic polynomial x2-6x+a .find the value of ,a, if 3alpha+2bita =20

Answer 1

Hi there!

Here's your answer :-

Given - α and β are roots of x² - 6x + a

→ Sum of roots of quad. polynomial = - b / a = - (-6) / 1 = 6

α + β = 6

α = 6 - β -----(i)

Now,

3α + 2β = 20

3(6 - β) + 2β = 20

18 - 3β + 2β = 20

-β = 2

β = -2

Substitutin' value of β in eqn. (i) :-

α = 6 - (-2) = 6 + 2 = 8

→ Product of roots of quad. polynomial = c / a

α × β = a / 1

a = 4 × (-2)

a = -8

Hence, The required answer is :- [ - 8 ]

Hope it helps!