1.)Find the value of k in the equation x2 - 2x + K - 1 = 0 if this equation has two equal roots.
2.) Find the value of k in the equation of the x²-4x+k+1 = 0 if this quadratic equation has no solution.
Big Thank You in advance :))
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1.)Find the value of k in the equation x2 - 2x + K - 1 = 0 if this equation has two equal roots.
2.) Find the value of k in the equation of the x²-4x+k+1 = 0 if this quadratic equation has no solution.
Big Thank You in advance :))
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1. If the equation has two equal roots, then the discriminant is equal to zero.
a=1 , b=2 , c=K-1
b²-4ac = 0
2²-4(1)(K-1) = 0
4 - 4K +1 = 0
3 - 4K = 0
K = -3/-4
K = 3/4
2. If the equation has no solution, then the discriminant is less than 0 .
a=1 , b=-4, c=k+1
b²-4ac < 0
(-4)² - 4(1)(k+1) < 0
16 - 4k -4 < 0
12 - 4k < 0
12 - 4k +12 < 0 + 12
-4k < 12
k > 12/-4
k > -3
hence, k is any value greater than -3 .