Class X ICSE Maths Chapter Quadratic Equations Exercise 5.4
Welcome to our comprehensive collection of questions on the topic "Quadratic Equations," designed to help you master this fundamental concept in algebra. Our question bank covers key topics such as solving quadratic equations using factorization, the quadratic formula, completing the square, and analyzing the nature of roots. These questions are ideal for students looking to strengthen their problem-solving skills and gain a deeper understanding of quadratic equations and their applications. Whether you're preparing for exams or enhancing your algebra skills, our resource provides the perfect platform to practice and excel in "Quadratic Equations."
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Q1 Find the discriminate of the following equations and hence find the nature of roots:
(i) 3x² - 5x - 2 = 0
(ii) 2x² - 3x + 5 = 0
(iii) 16x² - 40x + 25 = 0
(iv) 2x² + 15x + 30 = 0
Q2 Discuss the nature of the roots of the following quadratic equations:
(i)3x² - 4√3x + 4 = 0
(ii) x² - 1/2x + 4 = 0
(iii) - 2x² + x + 1 = 0
(iv) 2√3x² - 5x + √3 = 0
Q3 Find the nature of the roots of the following quadratic equations:
(i) x² - 1/2x - 1/2 = 0
(ii) x² - 2√3x - 1 = 0
If real roots exist, find them
Q4 Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots:
(i) px² - 4x + 3 = 0
(ii) x² + (p - 3)x + p = 0
Q5 Find the value (s) of k for which each of the following quadratic equation has equal roots:
(i) x² + 4kx + (k2 - k + 2) = 0
(ii) (k - 4)x2 + 2(k - 4)x + 4 = 0
Q6 Find the value(s) of m for which each of the following quadratic equation has real and equal roots:
(i) (3m + 1)x² + 2(m + 1)x + m = 0
(ii) x² + 2(m - 1) x + (m + 5) = 0
Q7 Find the values of k for which each of the following quadratic equation has equal roots:
9x² + kx + 1 = 0
x² - 2kx + 7k - 12 = 0
Also, find the roots for those values of k in each case.
Q8 Find the value(s) of p for which the quadratic equation (2p + 1)x² - (7p + 2)x + (7p - 3) = 0 has equal roots. Also find these roots
Q10 Find the least positive value of k for which the equation x² + kx + 4 = 0 has real roots
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