Question

check weather the equation 5x^2 - 6x -2 =0 has real roots and if it has, find them by the method of completing square. Also verify that roots obtained satisfy the given equation​

Answer 1

we have.,
$5x ^{2} - 6x - 2$
Using,
$d = b ^{2} - 4ac$
$(- 6)^{2} - 4 \times 5 \times ( - 2)$
D = 36+40 = 76

So, D = 76 >0

Hence, the roots of the given polynomial is real and distinct.

Now, using completing square method.

Roots are :-

x = √19+3/√5
&
x = -√19+3/√5

Verification is in the attachment.

Answer 2

Let P(x) =
$5x ^{2} - 6x - 2$
Finding D,
$d = b ^{2} - 4ac$
$d = ( - 6) ^{2} - 4 \times 5 \times ( - 2)$
$d = 36 + 40$
$d = 76$
Since, D >0.
Therefore, the roots of the given polynomial are real and distinct.

Roots are , √19+3/√5 & -√19+3/√5.

Verification is in the attachment.


Thanks........❤️