Question

If 5 is one of the zeros of polynomial p(x)=x³-6x² ax 10 then a=?

Answer 1

The value of a in the polynomial p(x) = x³ - 6x² + ax + 10, when 5 is a zero, is 3. This is found by substituting 5 into the polynomial and solving for a.

Step-by-step explanation:

To find the value of a in the polynomial p(x) = x³ - 6x² + ax + 10 when 5 is a zero, we use the fact that if 5 is a zero, then p(5) = 0. Substituting 5 into the polynomial gives us:

5³ - 6(5)² + 5a + 10 = 0

Solving this equation step by step:

• 5³ is 125
• 6(5)² is 6(25), which is 150
• Substituting these values in, we get 125 - 150 + 5a + 10 = 0
• Simplify to -25 + 5a + 10 = 0
• Combine like terms to get 5a - 15 = 0
• Finally, solving for a gives us a = 3

Therefore, a = 3 for the polynomial to have 5 as a zero.