Question

Q25)Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes

respectively.(i) 1/4 , -1​

Answer 1

Answer:

f(x) = 4x² - x - 4

Explanation:

$x_{1}$ + $x_{2}$ = $\frac{1}{4}$

$x_{1}$$x_{2}$ = - 1

$x_{1}$ = $\frac{1}{4}$ - $x_{2}$

($\frac{1}{4}$ - $x_{2}$)$x_{2}$ = -1

$\frac{1}{4}$ $x_{2}$  - $x_{2}$² = - 1

$x_{2}$² - $\frac{1}{4}$ $x_{2}$ - 1 = 0 ..... (1)

(1) × 4

4$x_{2}$² - $x_{2}$ - 4 = 0 ⇒ f(x) = 4x² - x - 4

Answer 2

:- Solution

➝ the formulas of sum and product of zeroes, we know,

➢ Sum of zeroes = α+β

➢ Product of zeroes = α β

➢ Sum of zeroes = α+β = 1/4

➢ Product of zeroes = α β = -1

➝ If α and β are zeroes of any quadratic polynomial, we written 0 directly

➢ x2–(α+β)x +αβ = 0

➢ x2–(1/4)x +(-1) = 0

➢ 4x2–x-4 = 0

➢Thus, the 4x2–x–4 is the quadratic