1. The zeroes of x2–2x –8 are:
(a) (2,-4)
(b) (4,-2)
(c) (-2,-2)
(d) (-4,-4)
Answer: (b) (4,-2)
2. What is the quadratic polynomial whose sum and the product of zeroes is √2, ⅓ respectively?
(a) 3x2-3√2x+1
(b) 3x2+3√2x+1
(c) 3x2+3√2x-1
(d) None of the above
Answer: (a) 3x2-3√2x+1
Explanation: Sum of zeroes = α + β =√2
Product of zeroes = α β = 1/3
∴ If α and β are zeroes of any quadratic polynomial, then the polynomial is;
x2–(α+β)x +αβ
= x2 –(√2)x + (1/3)
= 3x2-3√2x+1
3. If the zeroes of the quadratic polynomial ax2+bx+c, c≠0 are equal, then
(a) c and b have opposite signs
(b) c and a have opposite signs
(c) c and b have same signs
(d) c and a have same signs
Answer: (d) c and a have same signs
Explanation:
For equal roots, discriminant will be equal to zero.
b2 -4ac = 0
b2 = 4ac
ac = b2/4
ac>0 (as square of any number cannot be negative)
4. The degree of the polynomial, x4 – x2 +2 is
(a) 2
(b) 4
(c) 1
(d) 0
Answer: (b) 4
Explanation: Degree is the highest power of the variable in any polynomial.
If one of the zeroes of cubic polynomial is x3+ax2+bx+c is -1, then product of other two zeroes is:
(a) b-a-1
(b) b-a+1
(c) a-b+1
(d) a-b-1
Answer: (b) b-a+1
Explanation: Since one zero is -1, hence;
P(x) = x3+ax2+bx+c
P(-1) = (-1)3+a(-1)2+b(-1)+c
0 = -1+a-b+c
c=1-a+b
Product of zeroes, αβγ = -constant term/coefficient of x3
(-1)βγ = -c/1
c=βγ
βγ = b-a+1