Question

Determine whether the values given against the quadratic equation are the
roots of the equation or not.
x2 + 4x – 5 = 0. x = 1, -1.​

Answer 1

Answer:

Step-by-step explanation:

Given quadratic equation

p (x) = x square + 4x - 5

First put x = 1

p (1) = (1) square + 4 × 1 - 5 = 1 + 4 - 5 = 5 - 5 = 0

Hence x =1 is the root of the equation.

Now put x = -1

p ( -1 ) = ( -1 ) square + 4 × (-1) - 5 = 1 -4 - 5 = 1 -9 = -8.

Hence x = -1 is not a root of the equation.

Answer 2

Given :-

We have to check whether 1, -1 are roots of the Quadratic equation x² + 4x - 5 = 0

Solution:-

If they are roots of Quadratic equation If we Substitute their roots It should be equal to 0 So, lets verify

x² + 4x - 5 = 0

Case -1 : At x = 1

Substitute x = 1

x² + 4x - 5 = 0

(1)² + 4(1) - 5 = 0

1 + 4 - 5 = 0

5 - 5 = 0

0 = 0

Case -1 (Verified)

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Case - 2 At x = - 1

Substitute x = -1

x² + 4x - 5 = 0

(-1)² + 4(-1) - 5 = 0

1 - 4 - 5 = 0

1 -9 =0

-8 ≠ 0

So, 1 is the root of Quadratic equation Whereas -1 is not root

__________________________

Know more :-

Lets find the other root of Quadratic equation x² + 4x - 5 = 0

By using factorisation method

x² + 4x - 5 = 0

Splitting the middle term

x² + 5x - x - 5 = 0

x (x + 5 ) -1 (x + 5) =0

(x + 5) (x -1 ) = 0

Case :1

x + 5 = 0

x = -5

Case -2

x -1 =0

x = 1

So, the roots of Given Quadratic equation is. -5 , 1