JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

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Analyzing +4 | -1

Let

\alpha

and

\beta

be the roots of the equation

x^{2}-x-1=0

. If

p_{k}=(\alpha)^{k}+(\beta)^{k}, k \geq 1

, then which one of the following statements is not true?

View answer and explanation

Correct option: D

p_{5}=p_{2} \cdot p_{3}

Option D (

p_{5}=p_{2} \cdot p_{3}

) is not true because calculating

p_5

p_2

, and

p_3

shows that

p_5 = 11

while

p_2 \cdot p_3 = 12

, thus they are not equal.

More Questions from QUADRATIC EQUATIONS

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\alpha ,\beta

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\alpha ,\;\beta

{x^2} - px + q = 0

{\alpha _1},{\beta _1}

{x^2} - qx + p = 0,

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{x^2} + 4ax + 2 > 0

x

a

f\left( x \right) = a{x^2} + bx + c\;

\;f\left( { - 1} \right) < 1,f\left( 1 \right) > - 1,f\left( 3 \right) < - 4\;

\;a \ne 0,

9{x^2} - 18\left| x \right| + 5 = 0

f\left( x \right) = \log \left( {{x^2} - x - 2} \right)