We have been given, `2x^2-2sqrt2x+1=0` Now we also know that for an equation ax2 + bx + c = 0, the discriminant is given by the following equation: D = b2 - 4ac Now, according to the equation given to us, we have,a = 2, `b=-2sqrt2` and c = 1. Therefore, the discriminant is given as, `D=(-2sqrt2)^2-4(2)(1)` = 8 - 8 = 0 Since, in order for a quadratic equation to have real roots, D ≥ 0.Here we find that the equation satisfies this condition, hence it has real and equal roots. Now, the roots of an equation is given by the following equation, `x=(-b+-sqrtD)/(2a)` Therefore, the roots of the equation are given as follows, `x=(-(-2sqrt2)+-sqrt0)/(2(2))` `=(2sqrt2)/4` `=1/sqrt2` Therefore, the roots of the equation are real and equal and its value is `1/sqrt2` Page 2
We have been given, 3x2 - 5x + 2 = 0 Now we also know that for an equation ax2 + bx + c = 0, the discriminant is given by the following equation: D = b2 - 4ac Now, according to the equation given to us, we have,a = 3, b = -5 and c = 2. Therefore, the discriminant is given as, D = (-5)2 - 4(3)(2) = 25 - 24 = 1 Since, in order for a quadratic equation to have real roots, D ≥ 0.Here we find that the equation satisfies this condition, hence it has real roots. Now, the roots of an equation is given by the following equation, `x=(-b+-sqrtD)/(2a)` Therefore, the roots of the equation are given as follows, `x=(-(-5)+-sqrt1)/(2(3))` `=(5+-1)/6` Now we solve both cases for the two values of x. So, we have, `x=(5+1)/6` `=6/6` = 1 Also, `x=(5-1)/6` `=4/6` `=2/3` Therefore, the roots of the equation are `2/3` and 1. |