Question

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Find the zeros of the polynomial p(x) = (x - 5)(x2 - x - 6).​

Answer 1

Answer:

$\text{x}_{1}x </p><p>1$

= 5 and

$\text{x}_{2}x </p><p>2$

= 6

Step-by-step explanation:

p(x) = (x - 6)(x - 5)

Substitute the value of p(x) as 0, as we don't have value of x as given

⇒ 0 = (x - 6)(x - 5)

Switch the sides

⇒ (x - 6)(x - 5) = 0

Split into possible cases

⇒ x - 6 = 0

x - 5 = 0

Solve the equations

⇒ x = 6

x = 5

The final solutions are :

$⇒ \text{x}_{1}x </p><p>1$

$⇒ \text{x}_{1}x </p><p>1</p><p> = 5$

$\text{x}_{2}x </p><p>2</p><p> </p><p> = 6$

∴ The zeroes of the polynomial p(x) = (x - 6)(x - 5) are

$\text{x}_{1}x 1$

= 5 and \text{x}_{2}x

2

= 6