Question

if one root of quadratic equations x^2 +6x+k=0 is h + 2√6 .Find h and k .....Give step by step explanation plzz​

Answer 1

hope it helps..........

Answer 2

The value of h is -3 and value of k is -15.

Step-by-step explanation:

The given quadratic equation is

$x^2+6x+k=0$

Quadratic formula : If a quadratic equation is $ax^2+bx+c=0$, then the root of quadratic equations are

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

In the given equation a=1,b=6 adn c=k. Using quadratic formula we get

$x=\dfrac{-6\pm \sqrt{6^2-4(1)(k)}}{2(1)}$

$x=\dfrac{-6\pm \sqrt{36-4k}}{2}$

$x=\dfrac{-6\pm \sqrt{4(9-k)}}{2}$

$x=\dfrac{-6\pm 2\sqrt{9-k}}{2}$

$x=\dfrac{2(-3\pm \sqrt{9-k})}{2}$

$x=-3\pm \sqrt{9-k}$

The roots of the quadratic equation are $x=-3+\sqrt{9-k}$ and $x=-3-\sqrt{9-k}$.

It is given that one root of quadratic equation is $h + 2\sqrt6$.

$h + 2\sqrt6=-3+\sqrt{9-k}$

$h + \sqrt{4\times 6}=-3+\sqrt{9-k}$

$h + \sqrt{24}=-3+\sqrt{9-k}$

On comparing both sides we get

$h=-3$

$24=9-k\Rightarrow k=-15$

Therefore, the value of h is -3 and value of k is -15.

#Learn more

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