Practice Questions for Algebra - Quadratic Equations

1. PE 2 - Quadratic Equation | Algebra - Quadratic Equations

If one root of the equation ax² + bx + c = 0 is four times the other, then ___________

(a)
b² = 25ac
(b)
b² = 4ac
(c)
4b² = 25ac
(d)
None of these

2. PE 2 - Quadratic Equation | Algebra - Quadratic Equations

If f(x) = x² + 4x + 1 and g(x) = x + 3, then the roots of the quadratic equation g[f(x)] will be

(a)
-2, -2
(b)
2, -1
(c)
-5, 4
(d)
None of these

3. PE 2 - Quadratic Equation | Algebra - Quadratic Equations

The quadratic equation g(x) = (px² + qx + r), p ≠ 0, attains its maximum value at x = 5/3. Product of the roots of the equation g(x) is 6. What is the value of q/r?

(a)
-5/3
(b)
-5/9
(c)
0
(d)
Cannot be determined

4. PE 2 - Quadratic Equation | Algebra - Quadratic Equations

If ab + bc + ca = 0 and a, b, c are rational numbers then the roots of the equation (ab + bc – ca)x² + (bc + ca – ab)x + (ac + ab – bc) = 0 are

(a)
rational
(b)
irrational
(c)
non-real
(d)
Cannot be determined

5. PE 2 - Quadratic Equation | Algebra - Quadratic Equations

If the equations x² + 2ax + 3b = 0 and x² + 2bx + 3a = 0, have one root in common, then find the value of (a + b). a ≠ b

(a)
0
(b)
3/4
(c)
-3/4
(d)
Cannot be determined

6. PE 2 - Quadratic Equation | Algebra - Quadratic Equations

The condition that both the roots of quadratic equation ax² + bx + c = 0 are negative is

(a)
a and c have an opposite sign that of b
(b)
b and c have an a opposite sign that of a
(c)
a and b have an opposite sign that of c
(d)
a, b and c are all of same sign

7. PE 2 - Quadratic Equation | Algebra - Quadratic Equations

If α and ß are the roots of the equation ax² + bx + c = 0, then find the roots of the equation ab²x² + b²cx + c³ = 0

(a)
α²ß, ß²α
(b)
$- \frac{α^{2} ß}{α + ß}$ , $- \frac{α ß^{2}}{α + ß}$
(c)
None of these
(d)
Cannot be determined

8. PE 2 - Quadratic Equation | Algebra - Quadratic Equations

k is an integer satisfying k² ≤ 30. How many equations of the form x² + kx + 4 = 0 exist such that the roots are real and unequal?

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7 8 9 4 5 6 1 2 3 0 . -

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9. PE 2 - Quadratic Equation | Algebra - Quadratic Equations

If ${(\frac{x + 1}{x - 3})}^{4}$ - 2 ${(\frac{x + 1}{x - 3})}^{2}$ – 8 = 0, then how many possible values can x have?

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7 8 9 4 5 6 1 2 3 0 . -

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10. PE 2 - Quadratic Equation | Algebra - Quadratic Equations

A teacher wrote a quadratic equation of the form x² + bx + c = 0 on the board and asked his students to find the roots. One student copied the coefficient of x incorrectly and found the roots as 2 and 9. Another student copied the constant term incorrectly and found the roots as 4 and 5. Find the correct equation.

(a)
x² + 9x + 18 = 0
(b)
x² – 9x + 18 = 0
(c)
x² + 9x – 18 = 0
(d)
x² – 9x – 18 = 0

PE 2 - Quadratic Equation | Algebra - Quadratic Equations

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