Question

If alpha and beta are the zeros of the polynomial 4x2-5x-1 then find the value of a^2-b^2

Answer 1

Answer:

I hope it would help you

Answer 2

Answer:

Given:

⇒ If alpha and beta are the zeros of the polynomial 4x² - 5x-1.

Find:

⇒ Find the value of a² - b².

According to the question:

⇒ $\sf Alpha + Beta = \dfrac{5}{4} = Sum \: of \: zeros.$

⇒ $\sf \dfrac{-1}{4} = Product \: of \: zeros$

Calculations:

$\sf ⇒ (Alpha - Beta)^2 = (Alpha + Beta)^2 - (4 \: Alpha Beta)$

$\sf ⇒ (Alpha - Beta)^2 = (\dfrac{5}{4})^2 - 4 (\dfrac{-1}{4})$

$\sf ⇒(Alpha - Beta)^2 = \dfrac{25}{16} + 1$

$\sf ⇒(Alpha - Beta)^2 = \dfrac{25 + 16}{16}$

$\sf ⇒(Alpha - Beta)^2 = \dfrac{41}{6}$

$\sf ⇒(Alpha + Beta)^2 = (Alpha + Beta) (Alpha - Beta)$

$\sf ⇒ \dfrac{5}{4} \times \dfrac{\sqrt{41}}{4}$

⇒ ${\sf{\underline{\boxed{\green{\sf{ \dfrac{5 \sqrt{41}}{16}}}}}}}$