Quadratic Equations Test

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Quadratic Equations Test - 45

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Weekly Quiz Competition

Question 1
1 / -0

In quadratic equation $$ax^2 + bx + c = 0$$, If discriminant $$D = b^2 - 4ac$$, then roots of quadratic equation are :

A
real and distinct, if D > 0

B
real and equal (repeated roots), if D = 0

C
non-real (imaginary), if D < 0

D
none of the above
Question 2
1 / -0

Minimum value of the expression $$cos^{2} \theta -(6sin \theta . cos \theta )+3 sin^{2} \theta +2$$ , is -

A
$$4+\sqrt {10}$$

B
$$4-\sqrt {10}$$

C
0

D
4

Solution
Question 3
1 / -0

To expand $$\left(4 -\dfrac{3}{x^2}\right)^{\dfrac{-1}{2}}$$ as the sum of infinite series, then [x] is greater than

A
$$\dfrac{1}{\sqrt3}$$

B
$$\dfrac{sqrt3}{2}$$

C
2

D
1/2

Solution
Question 4
1 / -0

The sun of the values of $$x$$ satisfying the equation $${ \left( 31+8\sqrt { 150 } \right) }^{ { x }^{ 2 }-3 }+1={ \left( 32+8\sqrt { 150 } \right) }^{ { x }^{ 2 }-3 }$$ is

A
$$3$$

B
$$0$$

C
$$2$$

D
$$none\ of\ these$$

Solution
Question 5
1 / -0

What is the value of the discriminant for the quadratic equation:
$$\sqrt 2 {x^2} - 5x + \sqrt 2 = 0$$

A
$$-5$$

B
$$17$$

C
$$\sqrt 2 $$

D
$$2\sqrt 2 $$

Solution
Question 6
1 / -0

Find the roots of the following complenting the square.

A
$${x^2} - 4\sqrt {2x} + 6 = 0$$

B
$$3{x^2} + 11x + 10 = 0$$

C
$$2{x^2} + x + 4 = 0$$

D
$$4{x^2} + 4\sqrt {3x} + 3 = 0$$
Question 7
1 / -0

The discriminant of $$\sqrt{3}x^{2}-2\sqrt{2}x-2\sqrt{3}=0$$ is ......................

A
32

B
16

C
-32

D
-16

Solution
Question 8
1 / -0

Let $$\alpha ,\beta $$ be the roots of $$a{ x }^{ 2 }+bx+c=0(a\neq 0)$$ and $$\gamma ,\delta $$ be the roots of $$p{ x }^{ 2 }+qx+r=0(p\neq 0)$$, and $${ D }_{ 1 },{ D }_{ 2 }$$ be the respective discriminants of these equations. If $$\alpha ,\beta ,\gamma ,\delta $$ are in A.P., then $${ D }_{ 1 },{ D }_{ 2 }$$ equals

A
$$\frac { { a }^{ 2 } }{ { p }^{ 2 } } $$

B
$$\frac { { a }^{ 2 } }{ { b }^{ 2 } } $$

C
$$\frac { { b }^{ 2 } }{ { q }^{ 2 } } $$

D
$$\frac { { c }^{ 2 } }{ { r }^{ 2 } } $$

Solution
Question 9
1 / -0

Out of the following_____________is not a quadratic equation.

A
$$2{x^2} + \sqrt 6 x - 6 = 0$$

B
$$x\left( {3x + 2} \right) = \left( {x + 2} \right)\left( {x - 1} \right)$$

C
$$x\left( {x - 2} \right) + 3 = {x^2} + 3$$

D
$$\left( {x + 2} \right)\left( {x - 3} \right) = 0$$

Solution
Question 10
1 / -0

What is the standard form of quadratic equation $$9 = - {x^2} + 13x?$$

A
$${x^2} + y = 13x$$

B
$${x^2} + 13x - y = 0$$

C
$${x^2} + 13x - 9 = 0$$

D
$$ - {x^2} + 13x - 9 = 0$$