If the equation 2x2 - x - k - 0 and x2 -x2 - 1 - 0 have 2 common roots- then the value of k is

The correct option is D 2 Given quadratic equation are 2x^2+x+k=0 and x^2+x2 1=0 Since the given equation has two roots in common, so from the ...

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Standard XII

Mathematics

Real Valued Functions

If the equati...

Question

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

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Solution

The correct option is D $- 2$
Given quadratic equation are $2 x^{2} + x + k = 0$ and $x^{2} + \frac{x}{2} - 1 = 0$
Since the given equation has two roots in common, so from the condition
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$
$\Rightarrow \frac{2}{1} = \frac{1}{\frac{1}{2}} = \frac{k}{- 1}$
$\Rightarrow k = - 2$
Hence, option D is correct.

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If the equation 2x2+x+k=0 and x2+x2−1=0 have 2 common roots, then the value of k is

The correct option is D −2Given quadratic equation are 2x2+x+k=0 and x2+x2−1=0Since the given equation has two roots in common, so from the conditiona1a2=b1b2=c1c2⇒21=112=k−1⇒k=−2Hence, option D is correct.

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