Question

. Find a quadratic polynomial whose sum and product of the zeroes are -2V3,-9 respectively.
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Answer 1

S O L U T I O N :

Given,

• Sum of zeroes (α + β) = -2√3
• Product of zeroes (αβ) = -9

To Find,

• Quadratic polynomial.

Explanation,

We know that,

Quadratic polynomial,

=> x² - (α + β)x + αβ

[ Put the values ]

=> x² - (-2√3)x + (-9)

=> x² + 2√3x - 9

Therefore,

The quadratic polynomial is x² + 2√3x - 9.

For information,

• D < 0

Nature of roots :- Roots are not real and unequal.

• D > 0

Nature of roots :- Roots are real and unequal.

• D = 0

Nature of roots :- Roots are real and equal.