QUADRATIC EQUATIONS | class 10 | ex.4.3 #trending #2024 #mathematics #exam #education #ncert #puzzle

QUADRATIC EQUATIONS | class 10 | ex.4.3 #trending #2024 #mathematics #exam #education #ncert #puzzlechallenge 2. Find the values of k for each of the following quadratic equations so that they have two equal roots. (i) 2x2 + kx + 3 = 0 (ii) kx (x – 2) + 6 = 0 Solutions: (i) 2x2 + kx + 3 = 0 Comparing the given equation with ax2 + bx + c = 0, we get a = 2, b = k and c = 3 As we know, discriminant = b2 – 4ac = (k)2 – 4(2) (3) = k2 – 24 For equal roots, we know, Discriminant = 0 k2 – 24 = 0 k2 = 24 k = ±√24 = ±2√6 (ii) kx(x – 2) + 6 = 0 or kx2 – 2kx + 6 = 0 Comparing the given equation with ax2 + bx + c = 0, we get a = k, b = – 2k and c = 6 We know, Discriminant = b2 – 4ac = ( – 2k)2 – 4 (k) (6) = 4k2 – 24k For equal roots, we know, b2 – 4ac = 0 4k2 – 24k = 0 4k (k – 6) = 0 Either 4k = 0 or k = 6 = 0 k = 0 or k = 6 However, if k = 0, then the equation will not have the terms ‘x2‘ and ‘x‘. Therefore, if this equation has two equal roots, k should be 6 only. 3. Is it possible to design a rectangular mango grove whose length is twice its breadth and the area is 800 m2? If so, find its length and breadth. 4. Is the following situation possible? If so, determine their present ages. The sum of the ages of the two friends is 20 years. Four years ago, the product of their age in years was 48. 5. Is it possible to design a rectangular park with a perimeter of 80 and an area of 400 m2? If so, find its length and breadth.