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Quantitative Aptitude

Quadratic Equations

If p, q are t...

Question

If p, q are the roots of the equation $x^{2} - 3 x + 2 = 0$ , find the equation which has roots as (2p + 1) and (2q + 1).

x² – 8x + 12 = 0

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2x² – 8x + 15 =0

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2x² – 7x + 14 = 0

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x² – 8x + 15 = 0

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Solution

The correct option is D x² – 8x + 15 = 0
Given equation: $x^{2} - 3 x + 2 = 0$
with roots p, q

When the roots become 2p and 2q,
the equation becomes:
${(\frac{x}{2})}^{2} - 3 (\frac{x}{2}) + 2 = 0, x^{2} - 6 x + 8 = 0$

When the roots become
$(2 p + 1) & (2 q + 1)$
the equation becomes:

$(x - 1)^{2} - 6 (x - 1) + 8 = 0, x^{2} - 8 x + 15 = 0$ .
Hence option (D)

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Q. Choose the correct answers for the following questions.
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(6) Out of the following equations, find the equation having the sum of its roots –5.

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(b) −x² + 3x + 3 = 0

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If p, q are the roots of the equation x2−3x+2=0 , find the equation which has roots as (2p + 1) and (2q + 1).

The correct option is D x2 – 8x + 15 = 0Given equation: x2−3x+2=0 with roots p, q When the roots become 2p and 2q, the equation becomes: (x2)2−3(x2)+2=0,x2−6x+8=0 When the roots become (2p+1) & (2q+1) the equation becomes: (x−1)2−6(x−1)+8=0,x2−8x+15=0. Hence option (D)

If p, q are the roots of the equation $x^{2} - 3 x + 2 = 0$ , find the equation which has roots as (2p + 1) and (2q + 1).