Question

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

Answer 1

➤ Answer

• Quadratic polynomial = 2x² + x - 6.

➤ Given

• The sum and product of zeros of a quadratic polynomial are -½ and -3 respectively.

➤ To Find

• The quadratic polynomial.

➤ Step By Step Explanation

Given that the sum and product of zeros of a quadratic polynomial are -½ and -3 respectively. We need to find the quadratic polynomial.

So let's do it !!

➠ Formula Used

$\dag \underline{ \boxed{\sf{ \purple{{x}^{2} - ( \alpha + \beta)x + \alpha \beta}}}}$

➠ By substituting the values

Sum of zeros (α + β) = -½ and product of zeros (αβ) = -3

So let's substitute the values.

$\longmapsto\tt {x}^{2} - \bigg( \cfrac{ - 1}{2} \bigg)x + ( - 3) \\ \\\longmapsto\tt {x}^{2} + \cfrac{1}{2}x - 3 = 0 \\ \\\longmapsto\tt \cfrac{ {2x}^{2} + x - 6}{2} = 0 \\ \\\longmapsto\tt {2x}^{2} + x - 6 = 2 \times 0 \\ \\ \longmapsto\bf \green{ {2x}^{2} + x - 6}$

Therefore, the quadratic polynomial = 2x² + x - 6.

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