Quadratic Equations Test

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Quadratic Equations Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following could be the values of `x` after applying 'zero product rule' to the quadratic equation: x²= 81?

A
- 8, 9

B
- 9, 9

C
- 81, 0

D
0, - 18

E
- 1, - 9
Question 2
1 / -0

Which of the following is one of the roots of the quadratic equation 2b²- 2a²= 8y²- 8ay?

A
(a - b)/2

B
a/2

C
b/2

D
(b - a)/2

E
ab/2
Question 3
1 / -0

Which of the following sets of values is obtained by factorisation of the quadratic equation (22 - y) = 57/y?

A
(- 19, -3)

B
(- 9, 3)

C
(9, 3)

D
(3, 19)

E
(3, 2)
Question 4
1 / -0

Which of the following values of x satisfy the quadratic equation 2x²= 3x?

A
0, 2/3

B
0, 3/2

C
0, -2/3

D
-3/2, 0

E
1, 0
Question 5
1 / -0

The smallest value of \(k\) for which the equation \(x^{2}+k x+4=0\) has real roots, is:

A
-2

B
4

C
16

D
6

E
-3

Solution

For solving these kinds of questions we have to check whether the determinant of the quadratic equation is greater than or equal to zero.
Determinant \(=b^{2}-4 a c\) where \(a, b\) and \(c\) are constants of the equation \(a x^{2}+b x+c=0\)
Given equation:
\(x^{2}+k x+4=0\)
Comparing it with the standard equation, we have \(a=1, b=k\) and \(c=4\)
Now for real roots, \(k^{2}-4 \times 1 \times 4 \geq 0\)
For smallest value of \(\mathrm{k}\),
\(k^{2}-16=0\)
\(\Rightarrow k=\pm 4\)
Hence, the correct option is (B).
Question 6
1 / -0

Which of the following values of `x` satisfies the quadratic equation x(x - 16) = 132?

A
- 22

B
- 6

C
6

D
23

E
2
Question 7
1 / -0

Which of the following is the solution set of the quadratic equation 6y²- (11/) y + 1 = 0?

A
(1/, 3 /)

B
(1/3, 3/)

C
(1/3, 3/2)

D
(1/, 1/2)

E
(1/2, 3/2)
Question 8
1 / -0

Which of the following is the solution set of the quadratic equation pqy²/(y – 1) = (p + q)²?

A
[(p – q)/p, (p + q)/q]

B
[(p + q)/p, (p – q)/q]

C
[(p - q)/p, (p – q)/q]

D
[(p + q )/p, (p + q)/q]

E
[q/p, (p + q)/q]
Question 9
1 / -0

Which of the following is the solution set of the quadratic equation y = 5/(3y - 1) up to two decimal places?

A
(–1.47, –1.14)

B
(1.47, –1.14)

C
(–1.47, 1.14)

D
(1.47, 1.14)

E
(0.47, –1.14)
Question 10
1 / -0

The product of two consecutive positive integers is 462. What is the smaller integer?

A
27

B
23

C
21

D
31

E
33

Solution

Suppose the two consecutive integers be '\(x\)' and '\(x+1\)' respectively.
Then, According to the question, the product of the two numbers is 462.
\((x) \times(x+1)=462\)
\(\Rightarrow x^{2}+x-462=0\)
\(\Rightarrow x^{2}+22 x-21 x-462=0\)
\(\Rightarrow x(x+22)-21(x+22)=0\)
\(\Rightarrow(x-21)(x+22)=0\)
\(\Rightarrow {x}=21\)
\(\because {x}\) can't be negative according to the question.
\(\therefore\) The smaller integer is 21.
Hence, the correct option is (C).
Question 11
1 / -0

The roots of the quadratic equation 5x²- 14x - 3 = 0 are

A
1/5, 3

B
5, 1/3

C
- 1/5, 3

D
1/5, - 3

E
- 1/5, - 3
Question 12
1 / -0

Which of the following is the solution set of the quadratic equation ab (y²+ 1) = (a²+ b²) y, where a and b are real numbers?

A
(a, b)

B
(a, a/b)

C
(b/a, a/b)

D
(b, b/a)

E
(b/a, a)
Question 13
1 / -0

Which of the following is the solution set of the quadratic equation 6y²- 20y + 6 = 0?

A
(1, 3)

B
(1, 1)

C
(3, 3)

D
(1/3, 3)

E
(1/2, 3)
Question 14
1 / -0

Which of the following are the roots of the quadratic equation 3 - [5 / (2y + 1)] = 6 / (y + 1)?

A
3/2, - 2

B
- 2, 3/2

C
2, - 2/3

D
- 2, 2/3

E
- 2, - 3/2
Question 15
1 / -0

Which of the following is the required zero/zeroes of the polynomial y²- (1 + ) y + ?

A
1/ or 1.

B
1 or .

C
or 1/ .

D
1/ or 1/.

E
2 or .
Question 16
1 / -0

Which of the following values of `y` satisfies the quadratic equation [2 - (25 / 9y)] = 9y / 25?

A
25/9

B
9/25

C
3/5

D
5/3

E
5/29
Question 17
1 / -0

Which of the following is the solution set of the quadratic equation (2y – 5)/(3y – 7) = (y – 1)/(y + 1)?

A
4, 3

B
– 3, 4

C
– 4, 3

D
3/4, 1

E
– 3, – 4
Question 18
1 / -0

Which of the following values satisfies the quadratic equation (3/y) + 5/(y + 2) = 4/(y - 1)?

A
3

B
1/3

C
1/2

D
- 2

E
- 3
Question 19
1 / -0

Which of the following is one of the roots of the quadratic equation 12(1 - y²) = 7y?

A
4/3

B
-4/3

C
-3/4

D
-3

E
4