Advertisements
Advertisements
प्रश्न
Given that x + 2 and x + 3 are factors of 2x3 + ax2 + 7x - b. Determine the values of a and b.
Advertisements
उत्तर
If x + 2 is a factor is 2x3 + ax2 + 7x - b then x + 2 = 0, x = -2 in equation
2(-2)3 + a (-2)2 + 7(-2) - b = 0
2(-8) + a(4) + 7(-2) - b = 0
-16 + 4a - 14 - b = 0
4a - b = 30 ...(1)
Also given that x + 3 is a factor of
2x3 + ax2 + 7x - b, then x + 3 = 0
x = -3 in equation
2(-3)3 + a(-3)2 + 7(-3) - b = 0
2(-27) + a(9) + 7(-3) - b = 0
-54 + 9a - 21 - b = 0
9a - b = 75 ...(2)
Solving (1) and (2) we get
a = 9, b = 6.
संबंधित 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.
Find the values of m and n so that x – 1 and x + 2 both are factors of x3 + (3m + 1)x2 + nx – 18.
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.
If x + a is a common factor of expressions f(x) = x2 + px + q and g(x) = x2 + mx + n; show that : `a = (n - q)/(m - p)`
Prove that (5x - 4) is a factor of the polynomial f(x) = 5x3 - 4x2 - 5x +4. Hence factorize It completely.
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 + x2 + 3x + 175 and g(x) = x + 5.
Show that (2x + 1) is a factor of 4x3 + 12x2 + 11 x + 3 .Hence factorise 4x3 + 12x2 + 11x + 3.
Using factor theorem, show that (x – 5) is a factor of the polynomial
2x3 – 5x2 – 28x + 15
If p(a) = 0 then (x – a) is a ___________ of p(x)
If x – 3 is a factor of x2 + kx + 15; the value of k is ______.
