Quadratic Polynomial

Q.

Find the zeroes of the polynomial $x^2+\frac{1}{6}x-2$ and verify the relation between the coefficient and zeroes of the polynomial.

Q.

Find the zeros of the following quadratic polynomials $x^2-2x-8$ and verify the relationship between the zeros and the coefficients.

Q.

Find the zeroes of the quadratic polynomial $x^2+7x+12$ and verify the relationship between the zeroes and the coefficients of the polynomial.

Q. If $a,b,c$ are real numbers, then $a(a-b)+b(b-c)+c(c-a)=0,$ only if

1. $a+b+c=0$
2. $a-b-c=0$
3. $a=b=c$
4. Either $a=b$ or $b=c$ or $c=a$

Q. Let $f\left(x\right)=x^5+a{x}^3+bx.$ The remainder when $f\left(x\right)$ is divided by $x+1$ is $-3.$ Then the remainder when $f\left(x\right)$ is divided by $x^2-1,$ is

1. $3x$
2. $3$
3. $-3$
4. $-3x$

Q. A polynomial in which power of variable is 2, is called quadratic polynomial.

1. False
2. True

Q.

Under what conditions, the graph of quadratic polynomial $p\left(x\right)=a{x}^2+bx+c$ is an upward parabola or a downward parabola

Q. If the zeroes of monic cubic polynomial are $3,5$ and $6,$ then the cubic polynomial is

1. $2x^3-28x^2+126x-180$
2. $x^3-14x^2+63x-90$
3. $3x^3-42x^2+189x-270$
4. $2x^3-14x^2+60x-78$

Q. The number of distinct zeroes of the polynomial $f\left(x\right)=x^2-8x+16$ is

Q. The number of the distinct zeroes of the polynomial $f\left(x\right)=x(x-4{)}^3(x-3{)}^2(x-1)$ is

Q. The coordinates of the vertex of a parabola represented by $y=a{x}^2+bx+c$ is, . Take D as discriminant;

1. $(\frac{-b}{2a},\frac{D}{4a})$
2. $(\frac{-b}{2a},\frac{-D}{4a})$
3. $(\frac{b}{2a},\frac{-D}{4a})$
4. $(\frac{b}{2a},\frac{D}{4a})$

Q. The zeroes of the quadratic polynomial $f\left(x\right)=x^2+7x+10$ are

1. $-2,5$
2. $-5,2$
3. $-5,-2$
4. $2,5$

Q. Let $x,y\in Z$ such that $x^2-2x=y^2-2y+1010$. Then the number of pairs $(x,y)$ satisfying the equation is

1. only one
2. infinitely many
3. more than one but finite
4. no such pair is possible

Q.

Express the following algebraic expression in exponential form

$7\times 3\times p\times q$

Q. If $a,b,c$ are real numbers, then $a(a-b)+b(b-c)+c(c-a)=0,$ only if

1. $a+b+c=0$
2. $a=b=c$
3. Either $a=b$ or $b=c$ or $c=a$
4. $a-b-c=0$

Q. The vertex of the parabola $y+2=(x-3{)}^2$ is

1. (-3, 2)
2. (3, -2)
3. (-3, -2)
4. (3, 2)

Q. The zeroes of the polynomial $f\left(x\right)=6x^2-x-2$ is/are

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

Q. If the graph of the quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$ is


Then, the possible value(s) of $a$ can be

1. $3$
2. $0$
3. $-2$
4. $-5$

Q. If the graph of the quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$ is


Then, the possible value(s) of $a$ can be

1. $3$
2. $0$
3. $-2$
4. $-5$

Q. Which among the following is a cubic polynomial?

1. $x^3-3x^{-1}+5$
2. $2x^3+5x^2+6x+1$
3. $x^2+x+1$
4. $x^4+3x^3+4x^2-5x+4$

Q. The degree of the polynomial expression $f\left(x\right)=x^4+5\sqrt{2}x-\sqrt{2}$ is

Q.

State whether the following statement is True or False

Zeroes of $x^2-5x$are 0 and -5

1. True
2. False