If the equations 2x2-x-k-0 and x2-x2-1-0 have a common root- then the value of k is

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Properties of Conjugate of a Complex Number

If the equati...

Question

If the equations $2 x^{2} + x + k = 0$ and $x^{2} + \frac{x}{2} - 1 = 0$ have a common root, then the value of $k$ is

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Solution

The correct option is D $- 2$
Let the common root be $α$
Applying condition for common root,
$\frac{α^{2}}{1 (- 1) - \frac{1}{2} (k)} = \frac{α}{k (1) - 2 (- 1)} = \frac{1}{2 (\frac{1}{2}) - 1 (1)}$

$\frac{- 2^{2}}{(\frac{k}{2} + 1)} = \frac{α}{k + 2} = \frac{1}{0}$

$\Rightarrow k = - 2$

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If the equations 2x2+x+k=0 and x2+x2−1=0 have a common root, then the value of k is

The correct option is D −2 Let the common root be αApplying condition for common root,α21(−1)−12(k)=αk(1)−2(−1)=12(12)−1(1)−22(k2+1)=αk+2=10⇒k=−2

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The correct option is D $- 2$
Let the common root be $α$
Applying condition for common root,
$\frac{α^{2}}{1 (- 1) - \frac{1}{2} (k)} = \frac{α}{k (1) - 2 (- 1)} = \frac{1}{2 (\frac{1}{2}) - 1 (1)}$

$\frac{- 2^{2}}{(\frac{k}{2} + 1)} = \frac{α}{k + 2} = \frac{1}{0}$

$\Rightarrow k = - 2$