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.
Advertisements
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
Using the Factor Theorem, show that (x + 5) is a factor of 2x3 + 5x2 – 28x – 15. Hence, factorise the expression 2x3 + 5x2 – 28x – 15 completely.
Prove by factor theorem that
(3x-2) is a factor of 18x3 - 3x2 + 6x -12
Prove by factor theorem that
(x - 3) is a factor of 5x2 - 21 x +18
Prove that ( p-q) is a factor of (q - r)3 + (r - p) 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.
Find the value of a , if (x - a) is a factor of x3 - a2x + x + 2.
Show that (x – 2) is a factor of 3x2 – x – 10 Hence factorise 3x2 – x – 10.
Show that (x – 1) is a factor of x3 – 5x2 – x + 5 Hence factorise x3 – 5x2 – x + 5.
If mx2 – nx + 8 has x – 2 as a factor, then ______.
