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Q.

Statement-I If one of the root is a quadratic equation is real, then its second root is also real.
Statement-II For $a$ , $b \in R$ , then the roots of $(x - a) (x - b) = h^{2}$ are real and unequal.

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a

Statement I is False, Statement II is True

b

Statement I is True, Statement II is True

c

Statement I is True, Statement II is False

d

Statement I is False, Statement II is False

answer is A.

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Detailed Solution

STATEMENT_II

$(x - a) (x - b) = h^{2} \Rightarrow x^{2} - (a + b) x + a b - h^{2} = 0$

$Δ = {(- (a + b))}^{2} - 4 (a b - h^{2})$

$= {(a + b)}^{2} - 4 a b + 4 h^{2}$

$= {(a - b)}^{2} + 4 h^{2} > 0$

the roots of $(x - a) (x - b) = h^{2}$ are real and unequal.

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Statement-I If one of the root is a quadratic equation is real, then its second root is also real.Statement-II For a,b∈R , then the roots of (x−a)(x−b)=h2 are real and unequal.