In the following, determine whether the given quadratic equations have real roots and if so, find the roots: `2x^2-2sqrt(6)x+3=0` (ii) `3a^2x^2+8a b x+4b^2=0, a!=0`
Answered Feb 05, 2023
Correct Answer - `x=(-2b)/(3a)" or "x=(-2b)/(a)35.x=(4b^(2))/(a^(2))" or "x=(-3a^(2))/(b^(2))`
Correct Answer - `(x-2)`
Correct Answer - `sqrt(2)+sqrt(3)+sqrt(5)`
Correct Answer - `x=sqrt(6)" or "x=(-sqrt(2))/(sqrt(3))`
Correct Answer - `x=(sqrt(3))/(4)" or "x=(-2)/(sqrt(3))`
Correct Answer - `x=sqrt((2)/(3)),sqrt((2)/(3))`
Correct Answer - `x=(sqrt(3))/(2)" or "x=(1)/(sqrt(3))`
Correct Answer - (i) Real and unequal (ii) Real and equal (iii) Not real (iv) Not real (v) Real and eqal (vi) Not real
Correct Answer - (i) `k=0" or "k=1" "(ii)" "k=2`
Correct Answer - `k=(49)/(28)`
(i) 2x2 + 3x + k = 0 For real roots, b2 - 4ac ≥ 0 ⇒ 9 - 4 x 2 x k ≥ 0 ⇒ 8k ≤ 9 ⇒ k ≤ \(\frac{9}{8}\) ⇒ k ∈ (-∞, \(\frac{9}{8}\)]. (ii) 2x2 + x +...
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