Question

1. Solve the following quadratic equations by factorisation.
&
(x² - 15 x + 54 =0)​

Answer 1

Required Answer:-

Given Equation:

• x² - 15x + 54 = 0

To Find:

• The values of x.

Solution:

Given that,

→ x² - 15x + 54 = 0

We have to split -15x into two parts whose sum is -15x and product is 54x²

>> -6x - 9x = -15x and (-6x) × (-9x) = 54x²

→ x² - 6x - 9x + 54 = 0

Factoring out,

→ x(x - 6) - 9(x - 6) = 0

→ (x - 9)(x - 6) = 0

By zero-product rule,

→ Either (x - 9) = 0 or (x - 6) = 0

→ x = 6, 9

→ Hence, the values of x are 6 and 9.

Answer:

• x = 6, 9

•••♪

Answer 2

Answer:

${\large{\bf{\tt{Factorization:}}}}$

${x}^{2} - 15x + 54 = 0 \\ \\ = > {x}^{2} - 9x - 6x + 54 = 0 \\ \\ = > {x}(x - 9) - 6(x - 9) = 0 \\ \\ = > (x - 9) \times (x - 6) = 0 \\ \\ = > x - 9 = 0 \: \: or \: \: x - 6 = 0 \\ \\ = > x = 9 \: \: \: or \: \: \: x = 6$