CRE 2 - Discriminant and Roots of Quadratic Equation | Algebra - Quadratic Equations
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If roots of an equation ax2 + bx + c = 0 are positive, then which of the following is correct?
- (a)
Signs of a and b should be alike
- (b)
Signs of b and c should be alike
- (c)
Signs of a and c should be alike
- (d)
None of the above
Solution
Discuss
ReportWhat will be the nature of roots of the equation 3x2 + 7x + 2 = 0.
- (a)
Real and unequal
- (b)
Real and equal
- (c)
Imaginary
- (d)
None of these
For what value of a, are the roots of the quadratic equation: ax2 – 2(a – 2)x + 1 = 0 real and equal?
- (a)
a = 1 only
- (b)
a = 4 only
- (c)
a = 1 or 4
- (d)
None of these
For what value of a will the roots of the quadratic: x2 + ax + 1 = 0 are non-real?
- (a)
-4 < a < 4
- (b)
-2 < a < 2
- (c)
a > -2
- (d)
a < 2
If bx2 + cx + a = 0 has real and different roots, then
- (a)
c2 - 4ba = 0
- (b)
c2 - 4ba > 0
- (c)
c2 - 4ba < 0
- (d)
c2 - 4ba ≤ 0
If the roots of the equation x2 – px + q = 0 differ by 1, then which of the following is true?
- (a)
q2 = 4(q + 1)
- (b)
p2 = 4q + 1
- (c)
q2 = p + 4
- (d)
p2 = 4(q + 2)
The roots of the equation x2 + 2√3x + 4 = 0 are
- (a)
real and equal
- (b)
rational and equal
- (c)
rational and unequal
- (d)
imaginary
If one root of x2 + ax + 6 = 0 is 3, while the equation x2 + ax + b = 0 has equal roots, then the value of b is
- (a)
25/4
- (b)
4/25
- (c)
4
- (d)
1/4
If the roots of the quadratic equation 2x2 – 4x + a = 0 are real and unequal, then which one of the following is correct?
- (a)
a = 2
- (b)
a < 2
- (c)
a ≤ 2
- (d)
None of these
How many real values of x are there for which (x - 1)2 + (x - 2)2 + (x - 3)2 + (x - 4)2 = 0