PE 1 - Quadratic Equation | Algebra - Quadratic Equations
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Two numbers whose sum is 4 and the absolute value of whose difference is 10 are the roots of the equation
- (a)
x2 + 4x + 21 = 0
- (b)
x2 – 4x + 21 = 0
- (c)
x2 + 4x – 21 = 0
- (d)
x2 – 4x – 21 = 0
Solution
Discuss
ReportIf α and 1/ α are the two roots of the equation ax2 + bx + c = 0, then which of the following is always true?
- (a)
a = c
- (b)
c = b
- (c)
b = a
- (d)
b = ac
One root of x2 + ax – 27 = 0 is square of the other. Then the value of a is
- (a)
3
- (b)
6
- (c)
-6
- (d)
-3
If the roots, x1 and x2, of the quadratic equation x2 – 3x + p = 0 also satisfy the equation 5x2 – 4x1 = 51, then which of the following is true?
- (a)
p = -28
- (b)
x1 = 3, x2 = 9
- (c)
x1 = 6, x2 = 3
- (d)
None of these
If α, ß are the roots of the equation 3x2 – 4x – 6 = 0, find the equation whose roots are α2 + 1 and ß2 + 1.
- (a)
9x2 + 70x + 97 = 0
- (b)
9x2 - 70x + 97 = 0
- (c)
9x2 - 70x - 97 = 0
- (d)
9x2 + 70x - 97 = 0
If α and β are the roots of x2 + ax + b = 0, then what is the value of ?
- (a)
a2 - 4b
- (b)
(a2 - 4b)/2
- (c)
(a2 - 4b)/b2
- (d)
(a2 - 2b)/b2
Sum of the areas of two squares is 394 m2. If the difference of their perimeters is 8 m, find the sides of the two squares?
- (a)
9 m, 7 m
- (b)
15 m, 13 m
- (c)
18 m, 16 m
- (d)
10 m, 12 m
The equation x + = 5 has
- (a)
two real roots and one imaginary roots
- (b)
one real and one imaginary root
- (c)
two imaginary roots
- (d)
one real root
If p and q are the roots of the equation x2 + px + q = 0, then find the values of p and q.
- (a)
(0, 0)
- (b)
(1, -2)
- (c)
(1, 2)
- (d)
Both (a) and (b)