Question

factorise:-

${x}^{2} + 5x + 6$
$2a {}^{2} = 9a - 5$
$y {}^{2} + 3y - 10$
$x {}^{2} - \sqrt{3x} - 6$

​

Answer 1

1) x² + 5x + 6

2) 2a² = 9a + 5

3) y² + 3y - 10

4) x² - √3x - 6

_____________ [GIVEN]

• We have to find integers.

______________________________

Consider all the given equations in the form ax² + bx + c.

We have to find integers whose sum is 'b' and product is 'c'.

______________________________

1) x² + 5x + 6

Sum of b is 3 + 2 and product of c is 3 × 2

⇒x² + 3x + 2x + 6

⇒ x(x + 3) + 2(x + 3)

⇒ (x + 2) (x + 3)

______________________________

2) 2a² = 9a + 5

Sum of b is - 10 + 1 and product of c is - 10 × 1

⇒ 2a² - 9a - 5

⇒ 2a² - 10a + a - 5

⇒ 2a(a - 5) + 1(a - 5)

⇒ (2a + 1) (a - 5)

_______________________________

3) y² + 3y - 10

Sum of b is - 2 + 5 and product of c is - 2 × 5

⇒ y² - 2y + 5y - 10

⇒ y(y - 2) + 5(y - 2)

⇒ (y + 5) (y - 2)

______________________________

4) x² - √3x - 6

Sum of b is - 2√3 + √3 and product of c is - 2√3 × √3

⇒ x² - 2√3x + √3x - 6

⇒ x(x - 2√3) + √3(x - 2√3)

⇒ (x + √3) (x - 2√3)

______________________________

Answer 2

Step-by-step explanation:

hey mate 2)should be 2a^2=9a+5