Advertisements
Advertisements
Question
If the zeroes of the polynomial `f(x) = x^3 – 3x^2 + x + 1` are (a – b), a and (a + b), find the values of a and b.
Advertisements
Solution
By using the relationship between the zeroes of he quadratic polynomial.
We have, Sum of zeroes=`(-("Coefficient of" x^2))/("Coefficient of" x^3)`
∴ a – b + a + a + b=`-(-3)/1`
⇒ 3a = 3
⇒ a = 1
Now, Product of zeroes=`(-"(Constant term")/("Coefficient of" x^3)`
∴ (a – b) (a) (a + b)=`(-1)/1`
⇒ (1 – b) (1) (1 + b) = –1 [∵a =1]
⇒` 1 – b^2 = –1`
`⇒ b^2 = 2`
`⇒ b=+-sqrt2`
APPEARS IN
RELATED QUESTIONS
The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).
The graphs of y = p(x) are given in following figure, for some polynomials p(x). Find the number of zeroes of p(x).
Find the zeroes of the polynomial `f(x) = x^2 ˗ 2x ˗ 8` and verify the relation between its zeroes and coefficients
Find all the zeroes of `(2x^4 – 3x^3 – 5x2 + 9x – 3)`, it is being given that two of its zeroes are `sqrt3 and –sqrt3`.
If -2 is a zero of the polynomial `3x^2 + 4x + 2k` then find the value of k.
If the sum of the zeros of the quadratic polynomial `kx^2-3x + 5` is 1 write the value of k..
If one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is ______.
If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and –3, then ______.
If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is -1, then the product of the
other two zeroes is ______.
If x3 + 1 is divided by x2 + 5, then the possible degree of quotient is ______.
If one of the zeroes of the quadratic polynomial (k -1)x² + kx + 1 the value of k is ______.
If f(x) = 5x - 10 is divided by x – `sqrt2`, then the remainder will be ______.
If 4x² – 6x – m is divisible by x – 3, the value of m is exact divisor of ______.
The number of polynomials having zeroes as -2 and 5 is ______.
If the graph of a polynomial intersects the x-axis at exactly two points, it need not be a quadratic polynomial.
Which of the following is not the graph of a quadratic polynomial?
If α and β are the zeroes of the polynomial x2 – 1, then the value of (α + β) is ______.
The number of polynomials having zeroes – 3 and 4 is ______.
The given linear polynomial y = f(x) has
