X - -k-2 is a root of quadratic equation 2x2 - k - 6 x - 3k - 0

The correct option is A TrueSubstitute x = k/2 in the #160;quadratic equation 2x^2 + (k 6) x 3k = 0 2( k/2)^2 + (k 6)( k/2) 3 ...

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Standard X

Mathematics

Roots of a Quadratic Equation

x = -k/2 is a...

Question

$x = \frac{- k}{2}$ is a root of quadratic equation $2 x^{2} + (k - 6) x - 3 k = 0$

True

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False

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Solution

The correct option is A True
Substitute $x = \frac{- k}{2}$ in the quadratic equation $2 x^{2} + (k - 6) x - 3 k = 0$
$2 (\frac{- k}{2})^{2} + (k - 6) (\frac{- k}{2}) - 3 k$
$= \frac{k^{2}}{2} - \frac{k^{2}}{2} + 3 k - 3 k$
$= 0$
Thus, $\frac{- k}{2}$ is a root of the equation.

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Similar questions

Q. State whether x =

\frac{- k}{2}

is the root of the quadratic equation 2x² + (k – 6)x – 3k = 0

Q. If

- 5

is one root of quadratic equation

2 x^{2} + p x - 15 = 0

and roots of quadratic equation

p (x^{2} + x) + k = 0

is equal ,then find the value of

k

Q. If the roots of a quadratic equation

2 x^{2} + 5 x + 3 k = 0

is reciprocal to other then find the values of k.

Q. If -5 is a root of the quadratic equation

2 x^{2} + p x - 15 = 0

and the quadratic equation

p (x^{2} + x) + k = 0

has equal roots, find the value of k.

If $- 5$ is a root of the quadratic equation $2 x^{2} + p x - 15 = 0$ and the quadratic equation $p (x^{2} + x) + k = 0$ has equal roots, find the value of $k$ .

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x=−k2 is a root of quadratic equation 2x2+(k−6)x−3k=0

The correct option is A TrueSubstitute x=−k2 in the quadratic equation 2x2+(k−6)x−3k=02(−k2)2+(k−6)(−k2)−3k=k22−k22+3k−3k=0Thus, −k2 is a root of the equation.

$x = \frac{- k}{2}$ is a root of quadratic equation $2 x^{2} + (k - 6) x - 3 k = 0$

The correct option is A True
Substitute $x = \frac{- k}{2}$ in the quadratic equation $2 x^{2} + (k - 6) x - 3 k = 0$
$2 (\frac{- k}{2})^{2} + (k - 6) (\frac{- k}{2}) - 3 k$
$= \frac{k^{2}}{2} - \frac{k^{2}}{2} + 3 k - 3 k$
$= 0$
Thus, $\frac{- k}{2}$ is a root of the equation.