Kerala SSLC · Mathematics · Class 10

Second Degree Equations: Important Questions with Answers

These are 10 important multiple-choice questions from the Kerala SSLC Mathematics chapter “Second Degree Equations” (Kerala SCERT syllabus). Each one shows the correct answer and a short explanation of why it is right. Try answering before you read the answer. ExamSummary has 20 practice questions on this chapter in total.

1. Q1.What is the nature of the roots of the equation x² - 6x + 10 = 0?

   • A)Real and distinct
   • B)Real and equal
   • C)Imaginary
   • D)Rational

   Answer: C) Imaginary

   The discriminant D is calculated as b² - 4ac, which equals 36 - 40 = -4. Since D is less than zero, the equation has no real roots, meaning the roots are imaginary.

2. Q2.If α and β are the roots of 2x² + 5x - 3 = 0, what is the sum of the roots (α + β)?

   • A)-5/2
   • B)5/2
   • C)-3/2
   • D)3/2

   Answer: A) -5/2

   For a quadratic equation ax² + bx + c = 0, the sum of the roots is given by -b/a. Here, b is 5 and a is 2, so the sum is -5/2.

3. Q3.Two consecutive positive integers have a product of 90. Which equation represents this situation?

   • A)x² + x - 90 = 0
   • B)x² - x - 90 = 0
   • C)x² + x + 90 = 0
   • D)x² - x + 90 = 0

   Answer: A) x² + x - 90 = 0

   Let the integers be x and x + 1. Their product is x(x + 1) = 90, which simplifies to x² + x - 90 = 0.

4. Q4.Find the roots of the equation x² - 9 = 0.

   • A)3 only
   • B)-3 only
   • C)±3
   • D)No real roots

   Answer: C) ±3

   By rearranging, x² = 9. Taking the square root of both sides gives x = ±√9, which results in roots 3 and -3.

5. Q5.For what value(s) of k does the equation x² + kx + 9 = 0 have equal roots?

   • A)±3
   • B)±6
   • C)±9
   • D)0

   Answer: B) ±6

   For equal roots, the discriminant D must be zero. So, k² - 4(1)(9) = 0 implies k² = 36, giving k = ±6.

6. Q6.A train travels 300 km at a uniform speed. If the speed had been 5 km/h more, the journey would have taken 2 hours less. What is the original speed?

   • A)x² + 5x - 750 = 0
   • B)x² - 5x - 750 = 0
   • C)x² + 5x + 750 = 0
   • D)x² - 5x + 750 = 0

   Answer: A) x² + 5x - 750 = 0

   Let speed be x. Time difference equation is 300/x - 300/(x+5) = 2. Simplifying this leads to the quadratic equation x² + 5x - 750 = 0.

7. Q7.If the sum of the roots is -5 and the product is 6, what is the quadratic equation?

   • A)x² - 5x + 6 = 0
   • B)x² + 5x + 6 = 0
   • C)x² + 5x - 6 = 0
   • D)x² - 5x - 6 = 0

   Answer: B) x² + 5x + 6 = 0

   The standard form is x² - (sum)x + (product) = 0. Substituting the values gives x² - (-5)x + 6 = 0, which simplifies to x² + 5x + 6 = 0.

8. Q8.Which formula is used to find the roots of a general quadratic equation ax² + bx + c = 0?

   • A)x = (-b ± √(b² - 4ac)) / 2a
   • B)x = (-b ± √(b² + 4ac)) / 2a
   • C)x = (b ± √(b² - 4ac)) / 2a
   • D)x = (-b ± √(b² - 4ac)) / a

   Answer: A) x = (-b ± √(b² - 4ac)) / 2a

   The quadratic formula states that the roots are given by x = [-b ± √(b² - 4ac)] / 2a, derived from completing the square method.

9. Q9.If the roots of a quadratic equation are reciprocals of each other, what is the relationship between the constant term c and coefficient a?

   • A)c = a
   • B)c = -a
   • C)c = 0
   • D)c = 1

   Answer: A) c = a

   The product of the roots is c/a. If roots are reciprocals, their product is 1. Therefore, c/a = 1, which implies c = a.

10. Q10.In a right-angled triangle, the hypotenuse is 13 cm and the difference between the other two sides is 7 cm. Which equation finds the shorter side x?

    • A)x² + (x + 7)² = 13²
    • B)x² + (x - 7)² = 13²
    • C)x² - (x + 7)² = 13²
    • D)(x + 7)² - x² = 13²

    Answer: A) x² + (x + 7)² = 13²

    Using Pythagoras theorem, side² + side² = hyp². If sides are x and x + 7, then x² + (x + 7)² = 13².

All Kerala SSLC Mathematics chapters →