Question

The sum and product of the zeros of a quadratic polynomial are –1/2 and — 3 respectively. What is the quadratic polynomial?

Answer 1

||✪✪ QUESTION ✪✪||

The sum and product of the zeros of a quadratic polynomial are –1/2 and — 3 respectively. What is the quadratic polynomial ?

|| ★★ FORMULA USED ★★ ||

→ The sum of the roots of the Equation ax² + bx + c = 0 , is given by = (-b/a)

and ,

→ Product of roots of the Equation is given by = c/a.

Also,

→ Any Quadratic Equation can be written as x^2 - ( sum of roots )x + product of roots = 0

|| ✰✰ ANSWER ✰✰ ||

Given that,

→ sum of roots = (-1/2)

→ Product of roots = (-3)

So,

Quadratic Equation :- x² - ( sum of roots )x + product of roots = 0

→ x² - (-1/2)x + (-3) = 0

→ x² +(x/2) - 3 = 0

→ 2x² + x - 6 = 0

Hence, The required Quadratic Equation is 2x² + x - 6 = 0.

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Answer 2

Question :- The sum and product of the zeros of a quadratic polynomial are –1/2 and — 3 respectively. What is the quadratic polynomial?

Solution :-

Quadratic Equation with sum and product of roots = x² - sum of roots * x + Product of roots = 0

putting values ,,

=> x² - (-1/2)x + (-3) = 0

=> x² + x/2 - 3 = 0

=> 2x² + x - 6 = 0

So, The required Equation is 2x² + x - 6 = 0 .