Question

Find a quadratic polynomials the sum and the product of whose zeroes are 1/4 and -1/8 respectively

Answer 1

Answer:

hey mate

equation will be -8x^2+2x+1

Answer 2

The quadratic polynomial is -4x² + x + $\frac{1}{2}$

Step-by-step explanation:

Let the quadratic polynomial = ax² + bx + c

Given, sum of the zeros of quadratic polynomial = $\frac{1}{4}$

$\frac{-b}{a} = \frac{1}{4}\\=> a = -4b..................(i)$

Product of the zeros of quadratic polynomial = $\frac{-1}{8}$

$\frac{c}{a} = \frac{-1}{8}\\=> a = -8c........................(ii)$

Now, from equation(i) and (ii),

-4b = -8c

=> b = 2c

So, a : b : c = -4b : b : $\frac{b}{2}$ = -4 : 1 : $\frac{1}{2}$

a = -4, b = 1 and c = $\frac{1}{2}$

ax² + bx + c = -4x² + x + $\frac{1}{2}$

Hence, the quadratic polynomial is -4x² + x + $\frac{1}{2}$