Advertisements
Advertisements
Question
A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is ______.
Options
x2 + 3x + 2
x2 – 3x + 2
x2 – 3x – 2
x2 + 3x – 2
Advertisements
Solution
A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is x2 + 3x + 2.
Explanation:
Given that,
Sum of zeroes = – 3
Product of zeroes = 2
Quadratic Polynomial is given by:
x2 – (Sum of zeroes)x + (Product of zeroes)
So, P(x): x2 – (– 3) x + 2
Required Quadratic Polynomial is x2 + 3x + 2.
APPEARS IN
RELATED QUESTIONS
If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 ± `sqrt3` , find other zeroes
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α - β
If the sum of the zeros of the quadratic polynomial f(t) = kt2 + 2t + 3k is equal to their product, find the value of k.
Verify that 5, –2 and `1/3` are the zeroes of the cubic polynomial p(x) = (3x3 – 10x2 – 27x + 10) and verify the relation between its zeros and coefficients.
Find a cubic polynomial whose zeroes are 2, –3 and 4.
Find all the zeroes of (x4 + x3 – 23x2 – 3x + 60), if it is given that two of its zeroes are `sqrt(3)` and `-sqrt(3)`.
The polynomial which when divided by −x2 + x − 1 gives a quotient x − 2 and remainder 3, is
If 2 and `1/2` are the zeros of px2 + 5x + r, then ______.
If α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to ______.
For the cubic equation \[ ax^{3} + bx^{2} + cx + d = 0 \] with roots \[ \alpha, \beta, \gamma \], the sum of the roots \( \alpha + \beta + \gamma \) is:
