Let $a,\,\,b \in R$ be such that the equation $a{x^2} - 2bx + 15 = 0$ has a repeated root $\alpha .$ If $\alpha {\text{ }}\,\,{\text{and}}\,\,{\text{ }}\beta $ are the roots of the equation ${x^2} - 2bx + 21 = 0,$ then ${\alpha ^2} + {\beta ^2}$ is equal to

JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Easy

1 of 1

Analyzing +4 | -1

Let

a,\,\,b \in R

be such that the equation

a{x^2} - 2bx + 15 = 0

has a repeated root

\alpha .

\alpha {\text{ }}\,\,{\text{and}}\,\,{\text{ }}\beta

are the roots of the equation

{x^2} - 2bx + 21 = 0,

then

{\alpha ^2} + {\beta ^2}

is equal to

View answer and explanation

Correct option: B

Option B (58) is correct because by solving the repeated root equation and substituting into the second equation, we find the value of α² + β².

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