Advertisements
Advertisements
प्रश्न
Find the value of ‘k’ if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.
उत्तर
p(x) = x^3 + 2x^2 - kx + 10
For (x - 2) to be the factor of p(x) = x3 + 2x2 – kx + 10
p(2) = 0
Thus (2)3 + 2(2)2 – k(2) + 10 = 0
⇒ 8 + 8 – 2k + 10 = 0
⇒ k = 13
Thus p(x) becomes x3 + 2x2 –13x + 10
Now, (x+5) would be the factor of p(x) iff p(–5) = 0
p(–5) = (–5)3 + 2(–5)2 – 13(–5) + 10 = –125 + 50 + 65 + 10 = 0
Thus, (x + 5) is also a factor of p(x).
APPEARS IN
संबंधित प्रश्न
Prove by factor theorem that
(x-2) is a factor of 2x3- 7x -2
Prove that (x+ 1) is a factor of x3 - 6x2 + 5x + 12 and hence factorize it completely.
Using factor theorem, show that (x - 3) is a factor of x3 - 7x2 + 15x - 9, Hence, factorise the given expression completely.
Use factor theorem to factorise the following polynominals completely.
x3 + 2x2 – 5x – 6
If (3x – 2) is a factor of 3x3 – kx2 + 21x – 10, find the value of k.
If (x + 2) and (x – 3) are factors of x3 + ax + b, find the values of a and b. With these values of a and b, factorise the given expression.
If ax3 + 3x2 + bx – 3 has a factor (2x + 3) and leaves remainder – 3 when divided by (x + 2), find the values of a and b. With these values of a and b, factorise the given expression.
Determine whether (x – 1) is a factor of the following polynomials:
x3 + 5x2 – 10x + 4
Using factor theorem, show that (x – 5) is a factor of the polynomial
2x3 – 5x2 – 28x + 15
If x – 3 is a factor of p(x), then the remainder is
