Question

x2+√2x-24 please give me answer​

Answer 1

Given Quadratic polynomial → x² + √2x - 24

To factorise this polynomial find out 2 numbers such that:

• Their product is 24
• Their difference is √2

The 2 numbers which satisfy these conditions are

4√2 and 3√2

• Product = 4√2 × 3√2 = 12(√2)² = 12 × 2 = 24
• Difference = 4√2 - 3√2 = √2

Factorise this polynomial by splitting the middle term.

x² + √2x - 24 = 0

⇒ x² + 4√2x - 3√2x - 24 = 0

⇒ x(x + 4√2) - 3√2(x + 4√2) = 0

⇒ (x - 3√2) (x + 4√2) = 0

Hence the factors of x² + √2x - 24 are:

• (x - 3√2)
• (x - 3√2)(x + 4√2)