Quadratic Polynomial

Q.

The zeros of the quadratic polynomial $x^2+99x+127$ are:

1. Both positive

2. Both negative

3. One positive and one negative

4. Both equal

Q.

Solve x :$4x²-2(a²+b²)x+a²b²$

Q.

How many zeroes does a quadratic polynomial have?

Q. Find the root of equation 16x-10/x=27

Q.

Solve for x:-

x^2 +5x - (a^2+a-6)=0

Q. (x-3)(x-7)(x-12)<0 solve for real x in equalities

Q. Solve for x :
1/a+b+x = 1/a +1/b +1/x (a≠0, b≠0, x≠0).

Q.

If $2$ is a zero of both the polynomial, $3x^2+ax-14$ and $2x-b$, then value of $(a-2b)$ is,

1. -5

2. -4

3. -7

4. -6

Q.

Solve: ax + by = a - b

bx - ay = a + b

Q.

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them.

Equation: $3x^2-4\sqrt{3}x+4=0$

Q. If $x+\frac{1}{x}=2$ then the positive value of $\sqrt{x}+\frac{1}{\sqrt{x}}$ will be

1. $\sqrt{2}$
2. $2$
3. $\sqrt{2}+1$
4. $1$

Q.

if 3 is a solution of 3x²+(k-1)x+9=0, then k=?

Q.

Solve for $x:x^2-(2b-1)x+(b^2-b-20)=0$

Q.

If $a+b+c=8$ and $ab+bc+ca=20$, find the value of $a^3+b^3+c^3–3abc$.

1. 16
2. 32
3. 48
4. 64

Q. The graph of the polynomial f(x) = ax² + bx + c is as shown in Fig. 2.20. Write the value of b² − 4ac and the number of real zeros of f(x).

Q. Solve the following quadratic equations by factorization:

$\frac{1}{x-2}+\frac{2}{x-1}=\frac{6}{x},x\ne 0$

Q. For the quadratic equation x^{​​​​​​2}​​​​​-2x+1=0 find the value of x+1/x

Q. Solve the following quadratic equations by factorization:

$10x-\frac{1}{x}=3$

Q. The number of polynomials having zeroes −2 and 5 is

(a) 1 (b) 2 (c) 3 (d) more than 3

Q. Solve the following quadratic equations by factorization:

9x² − 3x − 2 = 0

Q.

Question 8
The quadratic equation $2x^2-\sqrt{5}x+1=0$ has
(A) two distinct real roots
(B) two equal real roots
(C) no real roots
(D) more than 2 real roots

Q. Match the following columns
$\begin{array}{cc}P\left(x\right)& \text{Type of Polynomial}\\ a)40x-323& 1)\text{Quadratic Polynomial}\\ b)x^3+456x^2-6x+11& 2)\text{Linear Polynomial}\\ c)91x^2-5x+\sqrt{2}& 3)\text{Cubic Polynomial}\end{array}$

1. a-2, b- 1, c -3
2. a-3, b- 2, c -1
3. a-1, b- 3, c -2
4. a-2, b- 3, c -1

Q.

Find a and b for which (a - 1)x + 3y = 2, 6x + (1 - 2b) y = 6 infinite solution.

1. a = -7, b= -4

2. a = 3, b = -1

3. a = -1, b = -4

4. a = 3, b = -4

Q. The discriminant of x^2 + 3x + 1 = 0 is

1. 10
2. 6
3. 5
4. 8

Q. solve x(x-2)(x-5)/(x+3)^2(15-2x)^5<0

Q.

A polynomial with one degree is called $\_\_\_$

Q.

If x = 2 is a root of equation x² + 3x - k = 0 then value of k is

1. 12

2. 10

3. 7

4. 8

Q. Solve the following quadratic equations by factorization method.
4y² + 4y +1 = 0

Q. Solve each of the following quadratic equations:

(2x − 3)(3x + 1) = 0

Q. If f(x) is a polynomial such that f(a) f(b) < 0, then what is the number of zeros lying between a and b?