If $x^{2}$ +px + q = 0 is the quadratic equation whose roots are a – 2 and b – 2 where a and b are the roots of $x^{2}$ - 3x + 1 =0, then

p = 1 , q = 5

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p = 1, q = - 5

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p = -1, q = 1

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None of these

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Solution

The correct option is D
None of these

a + b = 3, ab = 1 and –p = a – 2 + b – 2, q = (a – 2)(b – 2)

$\Rightarrow$ –p = a + b – 4, q = ab – 2(a + b) + 4

$\Rightarrow$ –p = 3 – 4 and q = 1 – 2(3) + 4 ⇒ (p, q) = (1, –1)

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If x2+px + q = 0 is the quadratic equation whose roots are a – 2 and b – 2 where a and b are the roots of x2 - 3x + 1 =0, then

The correct option is D None of these a + b = 3, ab = 1 and –p = a – 2 + b – 2, q = (a – 2)(b – 2) ⇒ –p = a + b – 4, q = ab – 2(a + b) + 4 ⇒ –p = 3 – 4 and q = 1 – 2(3) + 4 ⇒ (p, q) = (1, –1)

If $x^{2}$ +px + q = 0 is the quadratic equation whose roots are a – 2 and b – 2 where a and b are the roots of $x^{2}$ - 3x + 1 =0, then

The correct option is D
None of these

a + b = 3, ab = 1 and –p = a – 2 + b – 2, q = (a – 2)(b – 2)

$\Rightarrow$ –p = a + b – 4, q = ab – 2(a + b) + 4

$\Rightarrow$ –p = 3 – 4 and q = 1 – 2(3) + 4 ⇒ (p, q) = (1, –1)