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Quadratic equation
I. p2 +7p + 10 = 0 II. q2- q – 6 = 0
Question
In each question two equations are provided. On the basis of these you have to find out the relation between p and q. Give answer.
I. p
2
+7p + 10 = 0 II. q
2
- q – 6 = 0
A
if p = q
Correct Answer
Incorrect Answer
B
if p > q
Correct Answer
Incorrect Answer
C
if q > p
Correct Answer
Incorrect Answer
D
if p ≥ q
Correct Answer
Incorrect Answer
E
if q ≥ p
Correct Answer
Incorrect Answer
Solution
I. p
2
+7p + 10 = 0,
p
2
+ 5p + 2p + 10 + 6 = 0; or
p( p+5) + 2( p+5) = 0
(p+2)( p+5) = 0, or p = -2 or = -5,
II. q
2
- q – 6 = 0;
q
2
– 3q + 2q – 6 = 0
q(q-3) + 2(q -3) = 0 or, q = -2 or 3
Hence, q ≥ p
Alternate Method:
if signs of quadratic equation is +ve and +ve respectively then the roots of equation will be -ve and -ve.
So, roots of first equation = p = -2, -5
if signs of quadratic equation is -ve and -ve respectively then the roots of equation will be +ve and -ve. (note: -ve sign will come in smaller root)
So, roots of second equation = q = -2, 3
After comparing roots of quadratic eqution we can conclude that q ≥ p.
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Practice Next
More Quadratic equation Questions
I. 144x² - 163x - 65 = 0 II. 91y² - 128y -48 = 0
I. 2b
2
- 37b + 143 = 0 II. 2a
2
+ 15a - 143 = 0
I. 8x – 3y = 85 II. 4x – 5y = 67
I. 2x
2
+ 3x - 9 = 0 II. 3y
2
- y - 10 = 0
I. 35 y² + 58 y + 24 = 0 II. 21 x² + 37 x + 12 = 0
I. x
3
= 1728 II. y
2
– 15y + 56 = 0
I. x²= 961 II. y= √961
I. 12x
2
+ 22x + 8 = 0 II. 4y
2
- y − 3 = 0
I. 2x² - 15x + 13 = 0 II. 3y² - 6y + 3 = 0
I. 2x
2
+ 5x + 2 = 0 II. 4y
2
= 1
Relevant for Exams:
EPFO SSA (Social Security Assistant)
SIDBI Grade A (Assistant Manager)
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