If {x^2} + px + q = 0 is the quadratic equati | vedclass

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(D) Given that $a$ and $b$ are the roots of ${x^2} - 3x + 1 = 0$,we have $a + b = 3$ and $ab = 1$.The roots of the new equation ${x^2} + px + q = 0$ a

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None of these

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(D) Given that $a$ and $b$ are the roots of ${x^2} - 3x + 1 = 0$,we have $a + b = 3$ and $ab = 1$.The roots of the new equation ${x^2} + px + q = 0$ are $a - 2$ and $b - 2$.Using the relation between roots and coefficients:$-p = (a - 2) + (b - 2) = (a + b) - 4 = 3 - 4 = -1$,which implies $p = 1$.$q = (a - 2)(b - 2) = ab - 2(a + b) + 4 = 1 - 2(3) + 4 = 1 - 6 + 4 = -1$.Thus,$(p, q) = (1, -1)$.Since $(1, -1)$ is not among the given options,the correct answer is $D$.

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:

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