Advertisements
Advertisements
प्रश्न
For what value of a is (x − 5) a factor of x3 − 3x2 + ax − 10?
Advertisements
उत्तर
Let f(x) = x3 − 3x2 + ax − 10 be the given polynomial.
By factor theorem, (x-5)is the factor of f(x), if f (5) = 0
Therefore,
`f(5) = (5)^3 - 3(5)^2 + a(5) - 10 = 0`
` 125 - 75 + 5a - 10 = 0 `
`5a = -40`
a = -8
Hence, a = − 8.
APPEARS IN
संबंधित प्रश्न
Identify polynomials in the following:
`p(x)=2/3x^3-7/4x+9`
If `f(x)=2x^2-13x^2+17x+12` find `f(0)`
If `x = 2` is a root of the polynomial `f(x) = 2x2 – 3x + 7a` find the value of a.
f(x) = 2x3 − 9x2 + x + 12, g(x) = 3 − 2x
What must be added to 3x3 + x2 − 22x + 9 so that the result is exactly divisible by 3x2 + 7x − 6?
y3 − 2y2 − 29y − 42
Factorize of the following polynomials:
4x3 + 20x2 + 33x + 18 given that 2x + 3 is a factor.
x4 − 2x3 − 7x2 + 8x + 12
When x3 − 2x2 + ax − b is divided by x2 − 2x − 3, the remainder is x − 6. The values of a and b are respectively
(x+1) is a factor of xn + 1 only if
