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Quadratic .If a quadratic equation ax^2 + 8x + 9 = 0 has two equal roots what is the...
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The problem provides the information that the quadratic equation has two equal roots, hence its determinant, `Delta = b^2 - 4ac ` needs to be equal to zero, such that:
`Delta = 0 => b^2 - 4ac = 0`
You need to identify the coefficients of equation, such that:
`a = a, b = 8, c = 9 `
`Delta = 8^2 - 4*a*9 => 64 - 36a = 0=> -36a = -64 => a = 64/36`
`=> a = 16/9`
Hence, evaluating the leading coefficient, under the given conditions, yields `a = 16/9.`
Posted by sciencesolve on February 27, 2013 at 8:10 AM (Answer #3)
A quadratic equation has always 2 roots. When you say that the equation has "only one root", you are wrong. In fact, the equation has 2 equal roots.
ax^2 + 8x + 9 = 0
We'll use Viete's relations between coefficients and roots:
x1 + x2 = -8/a (1)
x1*x2 = 9/a (2)
But x1 = x2, because the roots are equal
x1 + x1 = -8/a
2x1 = -8/a
x1 = -4/a
x1^2 = 9/a => (-4/a)^2 = 9/a
We'll square raise and we'll subtract 9/a both sides:
16/a^2 - 9/a = 0
We'll eliminate the denominator:
16 - 9a = 0
9a = 16
We'll divide by 9 both sides:
a = 16/9
So, for the quadratic equatino to have 2 equal roots, the value of the coefficient a is 16/9.
Posted by giorgiana1976 on May 18, 2011 at 10:46 AM (Answer #2)
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