Question

The roots of equation x^2-3ax+b=0differ by 4 , then show that 9a^2=4b+16

Answer 1

Answer:

9a² = 4b + 16

Step-by-step explanation:

Given Equation is x² - 3ax + b = 0.

On comparing with ax² + bx + c = 0, we get

a = 1, b = -3a, c = b.

Let the roots be α,β.

Given that roots of the equation differ by 4.

⇒ α - β = 4.

(i) Sum of roots:

α + β = -b/a

α + β = -(-3a)/1

α + β = 3a

(ii) Product of roots:

αβ = c/a

αβ = b/1

αβ = b.

Now,

We know that (α + β)² = (α - β)² + 4αβ

⇒ (3a)² = (4)² + 4(b)

⇒ 9a² = 4b + 16.

Hope it helps!

Answer 2

let ,

for alpha=a

beta=b

a-b=4

_::a+b =3a

::a×b=b