# Quadratic Equation – Quiz 1

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# Quadratic Equation – Quiz 1

### Introduction

Quadratic Equation is one of important topic in Quantitative Aptitude Section. In Quadratic Equation - Quiz 1 article candidates can find a question with an answer. By solving this question candidates can improve and maintain, speed, and accuracy in the exams. The Quadratic Equation - Quiz 1 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

Directions: In the following questions, two equations numbered are given in variables x and y. You have to solve both the equations and find out the relationship between x and y. Then give answer accordingly-
Find out the relationship between x and y.
$4{x}^{2} + 3x - 27 = 0$ $3{y}^{2} - 20y + 32 = 0$

A. If x > y B. If x < y C. If x $\geq$ D. If x $\leq$

B
x =2.25, -3
y = $\frac {8}{3}$, 4
Put all values on number line and analyze the relationship
-3……..2.25……..$\frac {8}{3}$……….4

### Q2

Find the roots of the quadratic equation: ${x}^{2}$ + 2x - 15 = 0?
A. -5, 3 B. 3, 5 C. -3, 5 D. -3, -5

A
${x}^{2}$ + 2x - 15 = 0
x(x + 5) - 3(x + 5) = 0
(x - 3)(x + 5) = 0
x = 3 or x = -5.

### Q3

The roots of the equation $3{x}^{2}$ - 12x + 10 = 0 are?
A. rational and unequal B. complex C. real and equal D. irrational and unequal

D
The discriminant of the quadratic equation is ${(-12)}^{2}$ - 4(3)(10) i.e., 24. As this is positive but not a perfect square, the roots are irrational and unequal.

### Q4

If alpha and beta are the roots of the equation x² – 9x + 14 = 0 then find the value of ${A}^{2}$ + ${B}^{2}$.
A. 25 B. 28 C. 53 D. 81

C

### Q5

If the roots of a quadratic equation are 20 and -7, then find the equation?
A. ${x}^{2} + 13x - 140 = 0$ B. ${x}^{2} - 13x + 140 = 0$ C. ${x}^{2} - 13x - 140 = 0$ D. ${x}^{2} + 13x + 140 = 0$

C
Any quadratic equation is of the form
${x}^{2}$ - (sum of the roots)x + (product of the roots) = 0 ---- (1)
where x is a real variable. As sum of the roots is 13 and product of the roots is -140, the quadratic equation with roots as 20 and -7 is: ${x}^{2}$ - 13x - 140 = 0.