The roots of quadratic equation x² – 9 = 0 are

1

(a)

± 3

(b)

± 6

(c)

± 4

(d)

± 9

If x = -2 is a root of equation x² – 4x + K = 0 then value of K is

1

(a)

-8

(b)

8

(c)

-12

(d)

12

Which of the following is not a quadratic equation?

1

(a)

3x + 4 – 7x² = 0

(b)

z² – 2z = 0

(c)

5x +3y² = 0

(d)

5x² – 125 = 0

The condition for equation ax² + bx + c = 0 to be quadratic is

1

(a)

a ≠ 0

(b)

a > 0

(c)

a ≠ 0, b ≠ 0

(d)

a < 0

Solve 9x²= 36

1

(a)

±4

(b)

±6

(c)

2

(d)

±2

The discriminant of quadratic equation \(x^{2}+ax+ b = 0\) is .................... .

1

(a)

\(a^{2}-4b\)

The value of k for which the quadratic equation \(9x^{2} - 24x + k = 0\) is ................. .

1

(a)

16

Find the value of p, so that x = 2 is a root of the quadratic equation \(3x^{2} - px - 3 = 0\) .

1

(a)

Since x=2 is a root of given quadratic equation 
\(\therefore\) 3(2)²-P(2)-2=0
\(\Rightarrow\)  12-2p-2=0
\(\Rightarrow\)  p=5
Hence, the value of p is 5.

If x = - \(\frac{1}{2}\), is a solution of the quadratic equation 3x² + 2kx- 3 = 0, find the value of k

1

(a)

Putting x = -\(\frac{1}{2}\). in 3x² + 2kx - 3 = 0
\(3\left( -\frac { 1 }{ 2 } \right) ^{ 2 }+2k\left( -\frac { 1 }{ 2 } \right) -3=0\)
⇒ \(\frac{3}{4}\) - k- 3 = 0
⇒ k = \(\frac{3}{4}\)- 3
⇒ k = \(\frac{3-12}{4}\)
⇒ k = \(\frac{-9}{4}\)

Find the value of k, for which one root of the quadratic equation kx²- 14x + 8 = 0 is six times the other.

1

(a)

Let one root = \(\alpha \)
Other root = 6 \(\alpha \)
Sum of roots = \(\alpha \) + 6\(\alpha \) = \(\frac { 14 }{ k } \)
\(\Rightarrow 7\alpha =\frac { 14 }{ k } \)
Product of roots \(\alpha (6\alpha )=\frac { 8 }{ k } \)
\(\Rightarrow 6\alpha ^{ 2 }=\frac { 8 }{ k } \)
\(6\times \frac { 4 }{ k^{ 2 } } =\frac { 8 }{ k } \)
\(\Rightarrow \frac { 3 }{ k^{ 2 } } =\frac { 1 }{ k } \)
or 3k=k²
3k-k²
k[3-k]=0
k=0 or k=3
k=0 is not possible
Hence k=3

Check whether the following equations are quadratic: (2x+1)(x-3)=(x-1)²

1

(a)

(2x+1)(x-3)=(x-1)²
2x²-6x+x-3=x²-2x+1
x²-3x-4=0
Which is of the form ax²+bx+c=0
Hence, given equation is a quadratic equation.

Find the roots/solution of the quadratic equation by factorisation: x²-9x+20=0

1

(a)

Given equation is x²-9x+20=0
x²-5x-4x+20=0
x(x-5)-4(x-5)=0
(x-5)(x-4)=0
either x-5=0 or x-4=0
x=5 or x=4
x=4 or 5 are the roots/solution of the given quadratic equation

For what value of k, are the roots of the quadratic equation 3x²+2kx+27=0 real and equal.

1

(a)

D=b²-4ac
D=(2k)²-4X3X27=4k²-324
For real and equal roots, D=0
4k²-324=0
4k²=324
k²=\(324\over 4\)
k²=81
k=\(\pm 9\)

Write the nature of roots of quadratic equation \(4x^2+4\sqrt3x+3=0\)

1

(a)

Given equation is \(4x^2+4\sqrt3x+3=0\)
Here a=4, b=4\(\sqrt3\), c=3
D=b²-4ac=48-48=0
As D=0, the equation has real and equal roots.

Write the nature of the roots of quadratic equation 7x²-4x+3=0

1

(a)

Given quadratic equation is
7x²-4a+3=0
Here a=7,b=-4,c=3
D=b²-4ac
= (-4)²-4x7x3
= 16-84=-68
\(\therefore \)D<0 therefore given quadratic equation has no real roots.

Check whether the following are quadratic equations: x² + 3x + 1 = (x - 2)²

2

(a)

Check whether the following are quadratic equations: (x+2)³=2x(x²-1)

2

(a)

Check whether the following equation is quadratic or not: (x+1)(x+3)=(x-1)(x-4)

2

(a)

Check whether the following equation is quadratic or not: \(\sqrt{x^2+4}=(x^2+1)^2\)

2

(a)

Find two consecutive positive integers, sum of whose squares in 365.

2

(a)

Seven years ago Varun's age was five times the square of swati's age. Three years hence Swati's age will be two-fifth of Varun's age. Find their present ages.

3

(a)

 A 2-digit number is such that product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.

3

(a)

Rs.9,000 were divided equally among a certain number of persons. Had their been 20more persons, each would have got Rs.160 less. Find the original number of persons.

3

(a)

Find the roots of the quadratic equation \(3x^{2} - x - 7 = 0\)  by applying the quadratic formula.

3

(a)

Find the roots of the quadratic equation \(x^{2}-4x+1 = 0\)   by applying the quadratic formula.

3

(a)

In a flight of 2800km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100km/h and time increased by 30 minutes. Find the original duration of the flight.

5

(a)

If x = - 2 is a root of the equation 3x² + 7x + P = 0, find the value of k so that the roots of the equation x² + k(4x + k -1) + P = 0 are equal.

5

(a)