Roots of a Quadratic Equation

Q. If one zero of the polynomial $3x^2-8x+2k+1$ is seven times the other, then the value of $k$ is ___.

1. $-\frac{1}{2}$
2. $\frac{1}{2}$
3. $\frac{2}{3}$
4. $-\frac{2}{3}$

Q.

$\text{Find the zeroes of the polynomial}{x}^2-2.$

1. $\sqrt{2}\text{and}-\sqrt{5}$

2. $4\text{and}3$

3. $\sqrt{2}\text{and}-\sqrt{2}$

4. $-5\text{and}2$

Q.

If 1 is a zero of the polynomial p(x), then which of the following is correct?

1. p(1) = x

2. p(1) = 0

3. p(1) = 1

4. p(2) - p(1) = p(2)

Q.

If one root of the quadratic equation $2x^2+ax-6=0$ is 2, find the value of a.

1. -1

2. -5

3. 5

4. 3

Q. If the zeroes of the quadratic polynomial
$x^2+(a+1)x+b$ are 2 and -3, then

1. a = -7 and b = -1
2. a = 5 and b = -1
3. a = 2 and b = -6
4. a = 0 and b = -6

Q. A real number $\alpha$ is said to be the root of the quadratic equation $a{x}^2+bx+c=0$, if $a{\alpha }^2+b\alpha +c=0$

1. True
2. False

Q. The zeroes of the quadratic polynomial $a{x}^2+bx+c$ and the roots of the quadratic equation $a{x}^2+bx+c=0$ are equal.

1. True
2. False

Q. $\text{If one of the zeros of quadratic polynomial}(k-1)x^2+kx+1\text{is}-3,$
$\text{then find the value of}k.$

1. $\frac{4}{3}$
2. $-\frac{4}{3}$
3. $\frac{2}{3}$
4. $-\frac{2}{3}$

Q.

If one root of the equation $2x^2+ax+6=0$ is 3, then the value of a is ___________.

1. -8

2. 3

3. 5

4. 7

Q.

Find all the common zeroes of the polynomials $x^3+5x^2-9x-45$ and $x^3+8x^2+15x$.

1. 3

2. 5

3. -3

4. -5