# Quadratic Equation – Quiz 4

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# Quadratic Equation – Quiz 4

### Introduction

Quadratic Equation is one of important topic in Quantitative Aptitude Section. In Quadratic Equation – Quiz 4 article candidates can find questions with an answer. By solving this questions candidates can improve and maintain, speed, and accuracy in the exams. Quadratic Equation – Quiz 4 questions are very useful for different exams such as IBPS PO, Clerk, SSC CGL, SBI PO, NIACL Assistant, NICL AO, IBPS SO, RRB, Railways, Civil Services etc.

### Q1

If a and b are the roots of the equation ${x}^{2}$ - 9x + 20 = 0, find the value of ${a}^{2}$ + ${b}^{2}$ + ab?
A. -21 B. 1 C. 61 D. 21

C
${a}^{2}$ + ${b}^{2}$ + ab = ${a}^{2}$ + ${b}^{2}$ + 2ab - ab
i.e, ${(a + b)}^{2}$ + ab
from ${x}^{2}$ - 9x + 20 = 0, we have
a + b = 9 and ab = 20. Hence the value of required expression ${(9)}^{2}$ - 20 = 61.

### Q2

Find the value of $\frac{a}{b}$ + $\frac{b}{a}$, if a and b are the roots of the quadratic equation ${x}^{2}$ + 8x + 4 = 0?
A. 15 B. 14 C. 24 D. 26

B
$\frac{a}{b}$ + $\frac{b}{a}$ = $\frac{{a}^{2} + {b}^{2}}{ab}$ + $\frac{{a}^{2} + {b}^{2} + b + a}{ab}$
= $\frac{({(a + b)}^{2} - 2ab)}{ab}$
a + b = $\frac{-8}{1} = -8$
ab = $\frac{4}{1}$ = 4
Hence $\frac{a}{b}$ + $\frac{b}{a}$ = $\frac{({(-8)}^{2} - 2(4))}{4}$ = $\frac{56}{4}$ = 14

### Q3

A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook?
A. 10 B. 8 C. 15 D. 7.5

A
Let the price of each note book be Rs.x.
Let the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.
Hence xy = 300
$\Rightarrow$ y = $\frac{300}{x}$
(x + 5)(y - 10) = 300 $\Rightarrow$ xy + 5y - 10x - 50 = xy
$\Rightarrow$ 5($\frac{300}{x}$) - 10x - 50 = 0 $\Rightarrow$ - 150 + ${x}^{2}$ + 5x = 0
multiplying both sides by $\frac{- 1}{10 x}$
$\Rightarrow$ ${x}^{2}$ + 15x - 10x - 150 = 0
$\Rightarrow$ x(x + 15) - 10(x + 15) = 0
$\Rightarrow$ x = 10 or -15
As x > 0, x = 10.

### Q4

Find the roots of quadratic equation: 2${x}^{2}$ + 5x + 2 = 0?
A. -2, $\frac{-1}{2}$ B. 4, -1 C. 4, 1 D. 2, $\frac{-1}{2}$

A
2${x}^{2}$ + 5x + 2 = 0
2x(x + 2) + 1(x + 2) = 0
(x + 2)(2x + 1) = 0 $\Rightarrow$ x = -2, $\frac{-1}{2}$

### Q5

Find the roots of quadratic equation: ${x}^{2}$ + x - 42 = 0?
A. -6, 7 B. -8, 7 C. 14, -3 D. -7, 6

D
${x}^{2}$ + 7x - 6x + 42 = 0
x(x + 7) - 6(x + 7) = 0
(x + 7)(x - 6) = 0 $\Rightarrow$ x = -7, 6