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The sum and the product of the roots of a quadratic equation are 7 and 12 respectively. If the bigger root is halved and the smaller root is doubled, then what is the resulting quadratic equation ?

The sum and the product of the roots of a quadratic equation are 7 and 12 respectively. If the bigger root is halved and the smaller root is doubled, then what is the resulting quadratic equation ? Correct Answer x<span style="position: relative; line-height: 0; vertical-align: baseline; top: -0.5em;font-size:10.5px;">2</span> - 8x + 12 = 0

Given:

Sum of the roots = 7

Product of the roots = 12

Concept used:

x2 – (sum of roots)x + product of roots = 0

Calculation:

Let the roots of the given quadratic equation are α and β 

According to the question

α + β = 7   ----(i)

and α.β = 12    ----(ii)

On solving the above equations, we get

α = 4, β = 3

According to the question

New roots are α' = 4/2 = 2, β' = 3 × 2 = 6

⇒ α' + β' = 2 + 6 = 8

⇒ α'.β' = 2 × 6 = 12

So, Resulting quadratic equation is

x2 – (α' + β')x + α'.β' = 0

⇒ x2 – 8x + 12 = 0

∴ The resulting quadratic equation is x2 – 8x + 12 = 0

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