Q1:
Assertion (A): The degree of quadratic equation is always 2. Hence, x2 – 1 = 0 is pure quadratic equation.
Reason (R): An equation of the form ax2 + c = 0 is known as pure quadratic equation.
Q2:
Assertion (A): The product of two successive positive integral multiples of 5 is 300, then the two numbers are 15 and 20.
Reason (R): The product of two consecutive integrals is a multiple of 2.
Q3:
Assertion (A): In the expression: x can’t have values 3 and – 5
Reason (R): If discriminant D = b2 – 4ac > 0 then the roots of the quadratic equation ax2 + bx + c = 0 are real and unequal.
Q4:
Assertion (A): The equation 8x2 + 3kx + 2 = 0 has equal roots than the value of k is ±
Reason (R): The equation ax2 + bx + c = 0 has equal roots if D = b2 – 4ac = 0.
Q5:
Assertion (A): Values of x are a for a quadratic equation 2x2 + ax – a2 = 0.
Reason (R): For quadratic equation ax2 + ax + c = 0,
Q6:
Assertion (A): Sum of ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Then the difference between their ages is 16.
Reason (R): For quadratic equation ax2 + bx + c = 0,
Q7:
Assertion (A): The roots of the quadratic equation x2 + 2x + 2 = 0 are imaginary.
Reason (B): If discriminant D = b2 – 4ac < 0="" then="" the="" roots="" of="" the="" quadratic="" equation="" />2 + bx + c = 0 are imaginary.
Q8:
Assertion (A): If we solve the equation of the form 9(x+2) – 6.(3)(x+1) + 1 = 0, then x = – 2.
Reason (R): The equation of the form x2a + xb + b = 0 can’t be solved by quadratic formula.
Q9:
Assertion (A): The equation has no root.
Reason (R): x - 1 ≠ 0, then only above equation is defined.
Q10:
Assertion : The equation x2 + 3x+1 = (x - 2)2 is a quadratic equation.
Reason : Any equation of the form ax2 + bx + c = 0 where a ≠ 0 , is called a quadratic equation.
Q11:
Assertion : The values of x are a for a quadratic equation 2x2 +ax- a2 =0 .
Reason : For quadratic equation ax2 + bx+ c = 0
Q12:
Assertion : The value of k = 2 , if one root of the quadratic equation 6x2 -x- k = 0 is ⅔
Reason : The quadratic equation ax2 + bx + c = 0, a ≠ 0 a has two roots.
Q13:
Assertion : If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c =1
Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.
Q14:
Assertion : A quadratic equation ax2 + bx + c = 0 , has two distinct real roots, if b2 - 4ac >0 .
Reason : A quadratic equation can never be solved by using method of completing the squares.
Q15:
Assertion : 4x2 -12x+9 =0 has repeated roots.
Reason : The quadratic equation ax2 + bx + c = 0 have repeated roots if discriminant D > 0 .
Q16:
Assertion : (2x - l)2 - 4x2 + 5 = 0 is not a quadratic equation.
Reason : x = 0, 3 are the roots of the equation 2x2 -60x = 0.
Q17:
Assertion : The equation 8x2 + 23kx+0 = has equal roots then the value of k is
Reason : The equation ax2 + bx+ c = 0 has equal roots if D =b2 - 4ac =0
Q18:
Assertion : The roots of the quadratic equation x2 + 2x+2 = 0 are imaginary.
Reason : If discriminant D =b2 - 4ac <0 then="" the="" roots="" of="" quadratic="" equation="">2 + bx+ c = 0 are imaginary.
Q19:
Assertion : The equation 9x2 + 34kx + 4 = 0 has equal roots for k = + 4 .
Reason : If discriminant ‘D’ of a quadratic equation is equal to zero then the roots of equation are real and equal.
Q20:
Assertion : Sum and product of roots of 2x2 -35x+0 = are and
respectively.
Reason : If a and b are the roots of ax2 + bx + c = 0 , a ≠ 0 , then sum of roots = α +β = and product of roots
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