Question

find the Quadratic polynonial in each case
sum and product of
the zeros 1/4 1-1​

Answer 1

Given:

• Sum and product of the quadratic polynomial - 1/4, -1

To find:

• Quadratic polynomial?

Solution:

• Let's consider the polynomial as p(x) = ax² + bx + c and let it's zeroes be α and β.

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

« Finding the quadratic polynomial,

⇒ x² + (Sum of zeros)x + (product of zeros) = 0

⇒ x² + (-1/4)x + (-1) = 0

On simplifying,

⇒ x² - 1/4x - 1 = 0

⇒ 4x² - x - 4 = 0

∴ Hence, p(x) = 4x² - x - 4 is the quadratic polynomial.

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀★ More information :

• Standard form of a quadratic equation is : a² + bc + x = 0, & a ≠ 0.

• Factoring an equation means to expand the equation and take out two common factors.

• Example - 6x² - 4x - 2 = 0