Question

find the roots of the quadratic equation by factorisation and 2xsquare + x -6=0​

Answer 1

ANSWER:

• Zeros are -2 and 3/2.

GIVEN:

• P(x) = 2x²+x-6

TO FIND:

• Roots of the above expression.

SOLUTION:

=> 2x²+x-6 = 0

=> 2x²+4x-3x -6 = 0

=> (2x²+4x)+(-3x-6) = 0

=> 2x(x+2)-3(x+2) = 0

=> (x+2)(2x-3) = 0

Either (x+2) = 0

=> x = (-2)

Either (2x-3) = 0

=> 2x = 3

=> x = 3/2

Zeros are -2 and 3/2.

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab

Answer 2

$\huge\mathfrak{Answer:}$

Given:

• We have been given a quadratic polynomial (2x² + x - 6 = 0).

To Find:

• We need to find the zeroes of this polynomial.

Solution:

We have been given that,

p(x) = 2x² + x - 6 = 0.

We can find the zeroes of this polynomial by the method of splitting the middle term.

We need to find two such numbers whose sum is 1 and product is -12.

Two such numbers are +4 and -3.

Substituting the values, we have

2x² + 4x - 3x - 6 = 0

=> 2x(x + 2) - 3(x +2) = 0

=> (x + 2)(2x - 3) = 0

Either (x + 2) = 0 or (2x - 3) = 0.

When (x + 2) = 0

=> x = -2

When 2x - 3 = 0

=> 2x = 3

=> x = 3/2

Hence, zeroes of this polynomial are -2 and 3/2.