Question
I: √(100 x4 + 125x4) + 7x +
41/2 = -4x II: 3√(64y3) x 2y + 19y + 72 = -3y + √1600 If the smallest root of equation II is multiplied with 2, then which among the following/s is / are true? i. Resultant > - 4 ii. Resultant + 21 (1/2) = Multiple of 5 iii. Resultant is less than the smallest root of equation ISolution
I: √(100 x4 + 125x4) + 7x + 41/2 = -4x 15x2 + 11x + 2 = 0 If in quadratic equation both the signs are +ve, then both the roots will always come in -ve. so, x = -6/15, -5/15 II: 3√(64y3) x 2y + 19y + 72 = -3y + √1600 If in quadratic equation both the signs are +ve, then both the roots will always come in -ve. so, y = -18/8, -4/8 Now, the smallest root of equation II is multiplied with 2 then we get, y = -(18/8) x 2 = -9/2 Now, From i, Resultant > - 4 -4.5 < -4 So, i is false From ii, Resultant + 21 (1/2) = Multiple of 5 -9/2 + 43/2 = Multiple of 5 34/2 is not multiple of 5. Hence, ii is false. From iii, Resultant is less than the smallest root of equation I Smallest root of equation I = -6/15 Hence, -9/2 < -6/15 So, iii is True
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