Advertisements
Advertisements
Question
If α and β are the zeroes of the polynomial x2 – 1, then the value of (α + β) is ______.
Options
2
1
–1
0
Advertisements
Solution
If α and β are the zeroes of the polynomial x2 – 1, then the value of (α + β) is 0.
Explanation:
Sum of zeroes of the quadratic equation
ax2 + bx + c = 0 is `(-b)/a`
∴ Sum of zeroes of x2 – 1 = x2 + 0x – 1 = 0 is `(-0)/1` = 0
∴ α + β = 0
APPEARS IN
RELATED QUESTIONS
If -2 is a zero of the polynomial `3x^2 + 4x + 2k` then find the value of k.
If 𝛼 and 𝛽 be the zeroes of the polynomial `2x^2 - 7x + k` write the value of (𝛼 + 𝛽 + 𝛼𝛽).
Find the zeroes of the quadratic polynomial `f(x) = 4sqrt3x^2 + 5x – 2sqrt3`.
If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it ______.
If x3 + 1 is divided by x2 + 5, then the possible degree of quotient is ______.
If x3 + 11 is divided by x2 – 3, then the possible degree of remainder is ______.
If x4 + 3x2 + 7 is divided by 3x + 5, then the possible degrees of quotient and remainder are ______.
Consider the following statements.
- x – 2 is a factor of x3 – 3x² + 4x – 4.
- x + 1 is a factor of 2x3 + 4x + 6.
- x – 1 is a factor of x5 + x4 – x3 + x² -x + 1.
In these statements
The zeroes of the quadratic polynomial x2 + kx + k, k ≠ 0 ______.
The number of polynomials having zeroes – 3 and 4 is ______.
