Discriminant = (-10)2 - 4*5*(-2) = 100 + 40 > 0
So the quadratic has two real roots ie it crosses the x-axis twice.
Using the discriminant the possible values of k are -9 or 9
Using the discriminant of b^2 -4ac = 0 the value of k works out as -2
Using the quadratic equation formula: x = 8.42 or x = -1.42
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Equation: x^2 +2kx +10x +k^2 +5 = 0 Using the discriminant: (2k +10)^2 -4*1*(k^2 +5) = 0 Multiplying out the brackets: 4k^2 +40K +100 -4k^2 -20 = 0 Collecting like terms: 40k +80 = 0 => 40k = -80 => k = -80/40 Therefore the value of k = -2
Using the discriminant for a quadratic equation the value of k works out as plus or minus 12.
Using the discriminant the possible values of k are -9 or 9
Using the discriminant formula for a quadratic equation k has a value of 8/25 or maybe 0.
Using the discriminant of b^2 -4ac = 0 the value of k works out as -2
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Yes because when it is rearranged in the form of 3x2-6x+2 = 0 the discriminant b2-4ac of this quadratic equation is greater than zero which means that it will have two solutions. Using the quadratic equation formula will give these solutions for x as 0.422 or 1.577 both correct to three decimal places.
Equation: 6x^2 +2x +k = 0 Using the discriminant formula: k = 1/6 Using the quadratic equation formula: x = -1/6 Check: 6(-1/6)^2 +2(-1/6) +1/6 = 0
If: 2^x2 +5x = k Then: 2x^2 +5x -k = 0 Using and solving the discriminant: k = -3.125 Using and solving the quadratic equation: x = -1.25 Check: 2(-1.25)^2 +5(-1.25) = -3.125
Using the quadratic equation formula: x = 8.42 or x = -1.42
It can be solved by using the quadratic equation formula.
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If the discriminant > 0 then 2 distinct real solutions.If the discriminant = 0 then 1 double real solution.If the discriminant < 0 then no real solutions (though there are two complex solutions).