Graphical Representation of Quadratic Equation

Q.

Find a relation between $x\mathrm{and}y$ such that the point $P\left(x,y\right)$ is equidistant from the points $A\left(-5,3\right)\mathrm{and}B\left(7,2\right)$.

Q. If the equation x² − ax + 1 = 0 has two distinct roots, then

(a) |a| = 2
(b) |a| < 2
(c) |a| > 2
(d) None of these

Q.

Graph of the quadratic equation ax² + bx + c = 0 , with a > 0 , D < 0 is

1. 
2. 
3. 
4. 

Q.

What is transformation of quadratic equations?

Q. If graph of quadratic polynomial ax² + bx + c cuts positive direction of y-axis, then what is the sign of c?

Q.

Find the roots of the following quadratic equations:

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

Q.

If the line (3x+14y+7)+k(5x+7y+6)=0 is parallel to y-axis then the value of k is

1. −2

2. 2

3. 1/3

4. −3/5

Q.

Find a quadratic polynomial whose zeroes are:

$2+\sqrt{3},2-\sqrt{3}$

Q.

Find the value of $p$ so that the equation $3x^2-5x+2p=0$ has equal roots. Also, find the roots.

Q.

Match the following graphs to their nature of roots:

i) Real and distinct roots
ii) Non real roots
iii) Integer roots
iv) Real and equal roots

1. $A\to i,B\to iii,iv,C\to ii$

2. $A\to iv,B\to iii,C\to iii$

3. $A\to i,C\to iii,B\to ii$

4. $A\to i,iii,C\to ii,B\to iv$

Q.

If $2$ is a root of the equation $x^2+bx+12=0$ and the equation $x^2+bx+q=0$ has equal roots, then $q=$

1. $8$

2. $-8$

3. $16$

4. $-16$

Q. Match the following graphs to their nature of roots:

i) Real and distinct roots
ii) Non real roots
iii) Integer roots
iv) Real and equal roots

1. $A\to i,C\to iii,B\to ii$
2. $A\to i,B\to iii,ivC\to ii$
3. $A\to i,iii,C\to ii,B\to iv$
4. $A\to iv,B\to iii,C\to iii$

Q.

How to find coordinates of the polynomial given

Q.

What are quadratic equations?

Q.

Graph of the quadratic equation ax² + bx + c = 0 , with a < 0 , D = 0 is

1. 
2. 
3. 
4. 

Q.

Find the roots of the following quadratic equations:

(ii) $\sqrt{3}{x}^2-2\sqrt{2}x-2\sqrt{3}=0$

Q.

Match the following graphs to their nature of roots:

i) Real and distinct roots
ii) Non-real roots
iii) Real and equal roots

1. $A\to iv,B\to iii,C\to iii$

2. $A\to i,C\to iii,B\to ii$

3. $A\to i,B\to iii,C\to ii$

4. $A\to i,iii,C\to ii,B\to iv$

Q.

Find the value of ‘$p$’ for which the roots of the following equations are real and equal:

$4x^2+px+9=0$

Q.

Find a point on the y-axis which is equidistant from the points $(5,4)$ and $(-2,3)$.

Q.

Find the value of ‘$k$’ for which the following quadratic equation has real roots:

$k{x}^2+6x+1=0$

Q. Very-Short-Answer Questions

If 1 is a root of the equation $a{y}^2+ay+3=0$ and $y^2+y+b=0$ then find the value of ab. [CBSE 2012]

Q.

If roots of equation $\left(b-c\right)x^2+\left(c-a\right)x+\left(a-b\right)=0$ are equal then show that $2b=a+c$.

Q.

Determine the nature of the roots of the following equations.

(1)

(2)

(3)

(4)

(5)

(6)

Q. If the equation $\left(1+m^2\right)x^2+2mcx+\left(c^2-a^2\right)=0$ has equal roots, prove that c² = a²(1 + m²).

Q.

Find the value of ‘$k$’ for which the following quadratic equation has real roots:

$2x^2-5x-k=0$

Q. The product of a number and the one obtained by decreasing it by 7 is -12. Then, the possible values for the number are .

1. -3 and 2
2. 4 and 3
3. 2 and -4
4. -3 and -4

Q. What is the difference between root and solution of an equation?

Q.

For what positive values of ‘m’, roots of the following equations are equal, distinct and imaginary.

(1)

(2)

(3)

(4)

Q. If a, b, c are in GP, then the equations $a{x}^2+2bx+c=0$ and $d{x}^2+2ex+f=0$ have a common root, if $\frac{d}{a},\frac{e}{b},\frac{f}{c}$ are in

1. GP
2. HP
3. None of these
4. AP

Q.

Graph of the quadratic equation ax² + bx + c = 0 , with a < 0 , D > 0 is

1. 
2. 
3. 
4.