Question

if the polynomial equation is 2x² + x - 10 = 0 , then find its roots by factorisation method and find relationship between roots and coefficient ..!!​

Answer 1

Solution

Given :-

• Polynomial equation is , 2x² + x - 10 = 0

Find :-

• Its roots by factorisation method
• Relationship between roots and coefficient.

Explanation

We Have,

==> 2x² + x - 10 = 0

==> 2x² + 5x - 4x - 10 = 0

==> x(2x + 5) - 2( 2x + 5) = 0

==> (x - 2)(2x + 5) = 0

==> (x - 2) = 0 Or, (2x + 5) = 0

==> x = 2 Or, 2x = -5

==> x = 2 Or, x = -5/2

Let,

• First roots be (P) = 2
• second roots be (Q) = -5/2

Now, Calculate relationship between roots and its coefficient.

Using Formula

★ Sum of roots = -(Coefficient of x)/(coefficient of x²)

★ Product of roots = (Constant part)/(coefficient of x ²)

So,

==> sum of roots = -(1)/2

==> 2 - 5/2 = -1/2

==> (4 - 5)/2 = -1/2

==> -1/2 = -1/2

L.H.S. = R.H.S.

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Again

==> Product of roots = -10/2

==> 2 × -5/2 = 5

==> -5 = -5

L.H.S. = R.H.S.

That's Proved.

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