The roots of the equation $(x - a) (x - b) = b^{2}$ are

Real and equal

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Real and unequal

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Imaginary

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Equal

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Solution

The correct option is D Real and unequal
$(x - a) (x - b) = b^{2}$
$\Rightarrow x^{2} - (a + b) x + a b - b^{2} = 0$
$D = b^{12} - 4 a^{1} c^{1}$
$\Rightarrow (a + b)^{2} - 4 \times 1 \times (a b - b^{2}) = D$
$\Rightarrow D = a^{2} + b^{2} + 2 a b + 4 b^{2} - 4 a b$
$D = (a - b)^{2} + (2 b)^{2}$
As $D > 0 ∴ h a s R e a l & u n e q u a l r o o t s$

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Similar questions

Is the roots of the equation x² + 2cx + ab = 0 are real and unequal prove that the equation x² - 2(a + b) + a² + b² + 2c² = 0 has no real roots.

a \neq b

(x - a) (x - b) = b^{2}

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= 0

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