Advertisements
Advertisements
Question
If \[x = \frac{1}{2}\] is a zero of the polynomial f(x) = 8x3 + ax2 − 4x + 2, find the value of a.
Advertisements
Solution
Since `x = 1/2`is a zero of polynomial f(x).
Therefore `f(1/2) = 0`
` ⇒ 8(1/2)^3+ a(1/2)^2 - 4(1/2) + 2 = 0`
`⇒ 1 + a / 4 - 2 +2 = 0`
⇒` a = -4`
The value of a is -4.
APPEARS IN
RELATED QUESTIONS
Identify polynomials in the following:
`h(x)=x^4-x^(3/2)+x-1`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials
`p(x)=2x^2-x+4`
The polynomials ax3 + 3x2 − 3 and 2x3 − 5x + a when divided by (x − 4) leave the remainders R1 and R2 respectively. Find the values of the following cases, if 2R1 − R2 = 0.
Show that (x − 2), (x + 3) and (x − 4) are factors of x3 − 3x2 − 10x + 24.
Find the value of a such that (x − 4) is a factors of 5x3 − 7x2 − ax − 28.
Find the value of a, if x + 2 is a factor of 4x4 + 2x3 − 3x2 + 8x + 5a.
In the following two polynomials, find the value of a, if x − a is factor (x5 − a2x3 + 2x + a + 1).
Factorize of the following polynomials:
4x3 + 20x2 + 33x + 18 given that 2x + 3 is a factor.
If (x − 1) is a factor of polynomial f(x) but not of g(x) , then it must be a factor of
Factorise the following:
x² + 10x + 24
