Question

quadratic equation........

Answer 1

first let's find the values of k

here,
2(4)+2k+4=0
2k+12=0
k=-6
now apply the quadratic equation formula to find answers!!
+6-√36-32/2(2)
4/4
=1
That's your answer!!!!!
Hope you found it helpful.

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Answer 2

Answer: x = 1

Step-by-step explanation:

Question: If one root of the equation $2x^2 + kx + 4 = 0$ is 2, then the other root is?

1) Find the value of k

In the given question, We have been given only one possible value of x and we are told to find the other.

To solve it, we have to first find the value of k by using the root of the equaion, x = 2

So,

$2(2)^2 + k(2) + 4 = 0 \\2(4) + 2k + 4 = 0\\8 + 2k + 4 = 0\\12 + 2k = 0\\2k = -12\\k = \frac{-12}{2} \\k = -6$

∴Hence the value of k is -6

2) Using the value of k find the value of other root by formula method

We got the value of k as -6

Now, Lets find the other root through Formula method.

=> To start first check if the quadratic equation is in the form of $ax^2 + bx + c = 0$

After applying value of k we get,

$2x^2 -6x + 4 = 0$

Where a = 2, b = -6 and c = 4

Now Apply the formula for finding x.

Formula:-

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

$x = \frac{-(-6) \pm\sqrt{36 - 4(2)(4)}}{2(2)}$

$x = \frac{6 \pm\sqrt{36 - 32}}{4}$

$x = \frac{6 \pm\sqrt{4}}{4}$

$x = \frac{8}{4} = 2$  or  $x = \frac{4}{4} = 1$

∴ The final answer is x = 1 i.e Option (d)