If -4 is a root of the quadratic equation x^2+px-4=k and the quadratic equation x^2+px+k+0 has equal roots , find the value of k
sumatisrivastav:
plz write the second eq. again
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x² + p x + k = 0 has equal roots.
So discriminant p² - 4 k = 0 => k = p²/4
Substitute this value in the 1st equation.
x² + p x - 4 - p²/4 = 0
Since -4 is a root : 16 - 4 p - 4 - p²/4 =0
=> p² + 16 p - 48 = 0
=> p = - 8 + 4√7 or 8 - 4 √7
=> k = p²/4 = (48 - 16 p) / 4
k = 44 - 16√7 or 44 + 16 √7
So discriminant p² - 4 k = 0 => k = p²/4
Substitute this value in the 1st equation.
x² + p x - 4 - p²/4 = 0
Since -4 is a root : 16 - 4 p - 4 - p²/4 =0
=> p² + 16 p - 48 = 0
=> p = - 8 + 4√7 or 8 - 4 √7
=> k = p²/4 = (48 - 16 p) / 4
k = 44 - 16√7 or 44 + 16 √7
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plz refer to this attachment
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