Sum and Product of Roots of a Quadratic Equation
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Q.
A and B solved a quadratic equation. In solving it , A made a mistake in the constant term and obtained the roots as 5, -3 while B made a mistake in the coefficient of x and obtained the roots as 1, -3. The correct roots of the equation are
1, 3
-1, 3
-1, -3
1, -1
Q.
If one of the roots of equation is and one of the roots of the equation is three times the other root, then the value of is
Q. Find the quadratic polynomial whose one zero is 5 and the product of roots is 30.
Q. If the product of the zeros of the quadratic polynomial
p(x)=(k−2)x2−4x+k, is 3, find the value of k.
Q. Find the zeroes of the following polynomials by factorisation method :
4x2−3x−1.
4x2−3x−1.
- −14
- 1
- 14
- −1
Q. The roots of the quadratic equation 3x2+2x−1=0 are .
- -1, 13
- -2, 13
- 1, 13
- 2, 3
Q. Find the product of roots of the quadratic equation x2+24x+36=0
- 36
- 32
- −23
- -24
Q. If equation (a2−4)x2+(a2−6a+8)x+(a2−3a+2)=0 has more than two roots then a is
Q. If one of the roots of the equation ax2+bx+c=0 is reciprocal of the other, choose the correct option.
- a=c2
- c = a
- c = 2a
- c=a2
Q. Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases:
(vi) f(x)=x2, x=0
(vi) f(x)=x2, x=0
Q.
The ratio of the sum and the product of the roots of 5x2–14x+8=0 is
5:8
7:4
9:11
6:5
Q. Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients.
49x2−81
- 17, −97
- 37, −97
- 137, −97
- 97, −97
Q. ___.
The ratio of the sum and the product of the roots of 5x2–14x+8=0 is
Q. ___.
The sum of the roots of the equation x2–8x+2=0 is
Q. If α=3, β=5 and γ=−8 then the value of α3+β3+γ3 is
- -240
- 0
- -360
- 240
Q. Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases:
(viii) f(x)=2x+1, x=−12
(viii) f(x)=2x+1, x=−12
Q. If √5−i√7 is a root of ax4+bx3+cx2+dx+e=0 , where a, b, c, d, e are rational numbers, then the other roots are:
- √5+i√7, 23, 13
- √5+i√7, −23, 13
- √5+i√7, −√5+i√7, −√5−i√7
- √5+i√7, 23, −13
Q. Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases:
(v) f(x)=5x−π, x=45
(v) f(x)=5x−π, x=45
Q. Find the zeros of the polynomial 6x3−7x2−11x+12, if x−1 is a factor of the polynomial.
Q. Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases:
(vii) f(x)=lx+m, x=−ml
(vii) f(x)=lx+m, x=−ml