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Quadratic Equation

Theory and Formula


Question


Q1. -4x2 + 6x -18 = 0 , this quadratic equation will open ___________

(a) downward (b) upwards (c) None of these (d) Can't say

Solution.
(a) downward
Solution

Q2. Which number is added both side to solve a equation x2 + (b/a)x + c/a = 0 by completing the square.

(a) b/2a (b) b/2c (c) (2a/c)2 (d) (b/2a)2

Solution.
(d) (b/2a)2
Solution

Q3. At the time of solving equation 9x2 - 15x + 6 = 0 by the method of completing the square which number is to be added both sides.

(a) (1/6)2 (b) 1/5 (c) (5/6)2 (d) (6/5)2

Solution.
(c) (5/6)2
Solution

Q4. If b2 - 4ac (Discriminant) is a perfect square but not equal to zero, than the roots are:

(a) Imaginary
(b) real equal
(c) real irrational and equal.
(d) real, rational and unequal.

Solution.
(d) real, rational and unequal.
Solution

Q5. x2 - 5x + k = 0 has real and equal roots if k is _________.

(a) 5 (b) 25 (c) 4 (d) 25/4

Solution.
Discriminant (D) = 0
b2 - 4ac = 0
25 - 4 x 1 x k = 0
25 = 4k
k = 25/4
Solution

Q6. The sum of two numbers is 15. If the sum of their recipocals is 3/10, find the numbers .

(a) 7,8 (b) 9,6 (c) 10,5 (d) 12,3

Solution.
Let the numbers be x and 15 - x.
then 1/x + 1/15 - x = 3/10
after solving we get x = 10 or 5
Solution

Q7. In a quadratic equation x2 + px + q = 0 , (2 - √3) is a root of this equation find the value of p and q.

(a) (3,2) (b) (4,1) (c) (2,3) (d) (-4,1)

Solution.
(d) (-4,1)
Solution

Q8. α and β are the roots of the equation 2x2 + 3x + 7 = 0 , find the value of α/β + β/α is .

(a) 6/7 (b) -19/14 (c) 9/4 (d) -2/3

Solution.
(b) -19/14
Solution

Q9. Curve of the quadratic equation 2x2 + 4x + 1 opens __________.

(a) upwards (b) downward (c) can't say

Solution.
(a) upwards
Solution

Q10. For which value of C the equation ax2 + 2bx + C = 0 has real and equal roots.

(a) b/a (b) b2/a (c) a/b (d) a2/b

Solution.
b2 - 4ac = 0

4b2 - 4ac = 0

b2 = ac

C = b2/a
Solution