Advertisements
Advertisements
प्रश्न
If x – 3 is a factor of x2 + kx + 15; the value of k is ______.
पर्याय
8
3
– 5
– 8
Advertisements
उत्तर
If x – 3 is a factor of x2 + kx + 15; the value of k is – 8.
Explanation:
Let f(x) = x2 + kx + 15
Given x – 3 is a factor of f(x)
∴ f(3) = 0
`\implies` 32 + k × 3 + 15 = 0
`\implies` 9 + 3k + 15 = 0
`\implies` 3k + 24 = 0
`\implies` 3k = – 24
`\implies` k = – 8
संबंधित प्रश्न
Find the values of m and n so that x – 1 and x + 2 both are factors of x3 + (3m + 1)x2 + nx – 18.
Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1).
By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.
p(x) = 2x3 − x2 − 45, q(x) = x − 3
Prove that (x-3) is a factor of x3 - x2 - 9x +9 and hence factorize it completely.
Prove that (x+ 1) is a factor of x3 - 6x2 + 5x + 12 and hence factorize it completely.
The expression 2x3 + ax2 + bx - 2 leaves the remainder 7 and 0 when divided by (2x - 3) and (x + 2) respectively calculate the value of a and b. With these value of a and b factorise the expression completely.
What number should be subtracted from 2x3 – 5x2 + 5x so that the resulting polynomial has 2x – 3 as a factor?
If (2x – 3) is a factor of 6x2 + x + a, find the value of a. With this value of a, factorise the given expression.
If x – 3 is a factor of p(x), then the remainder is
Factors of 4 + 4x – x2 – x3 are ______.
