In the following, determine whether the given quadratic equations have real roots and if so, find the roots:(i) 16x2 = 24x + 1(ii) x2 + x + 2 = 0(iii) 3x2+10x-83=0(iv) 3x2 − 2x + 2 = 0(v) 2x2-26x+3=0(vi) 3a2x2+8abx+4b2=0, a≠0(vii) 3x2+25x-5=0(viii) x2 − 2x + 1 = 0(ix) 2x2+53x+6=0(x) 2x2+7x+52=0(xi) 2x2-22x+1=0(xii) 3x2 − 5x + 2 = 0

In the following, determine whether the given quadratic equations have

1.	In the following, determine whether the given quadratic equations have real roots and if so, find the roots:(i) 16x2 = 24x + 1(ii) x2 + x + 2 = 0(iii) 3x2+10x-83=0(iv) 3x2 − 2x + 2 = 0(v) 2x2-26x+3=0(vi) 3a2x2+8abx+4b2=0, a≠0(vii) 3x2+25x-5=0(viii) x2 − 2x + 1 = 0(ix) 2x2+53x+6=0(x) 2x2+7x+52=0(xi) 2x2-22x+1=0(xii) 3x2 − 5x + 2 = 0
Answer» In the following, determine whether the given quadratic equations have real roots and if so, find the roots: (i) 16x² = 24x + 1 (ii) x² + x + 2 = 0 (iii) $\sqrt{3} x^{2} + 10 x - 8 \sqrt{3} = 0$ (iv) 3x² − 2x + 2 = 0 (v) $2 x^{2} - 2 \sqrt{6} x + 3 = 0$ (vi) $3 a^{2} x^{2} + 8 a b x + 4 b^{2} = 0, a \neq 0$ (vii) $3 x^{2} + 2 \sqrt{5} x - 5 = 0$ (viii) x² − 2x + 1 = 0 (ix) $2 x^{2} + 5 \sqrt{3} x + 6 = 0$ (x) $\sqrt{2} x^{2} + 7 x + 5 \sqrt{2} = 0$ (xi) $2 x^{2} - 2 \sqrt{2} x + 1 = 0$ (xii) 3x² − 5x + 2 = 0

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