How do you find the nature of the roots using the discriminant given 5−7x2+2x=0?
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Answered by
0
The roots of the equation are rational and unequal.
Disc. = (2)² - 4(-7)(5)
= 4 + 140
= 144>0 and perfect square
Answered by
2
7x² + 2x - 5 = 0
D = b² - 4ac
D = 2² - 4(7)(-5)
D = 4 + 140
D = 144
D is positive, therefore, the equation has two distinct real roots.
Now,
x = [-b ± sqrt(D)] / 2a
x = [-2 ± sqrt(144)]/2×7
x =( - 2 ± 12) /14
x = (-2 + 12) /14 or x=(-2-12)/14
x = 10/14 or x= - 14/14
x = 5/7 or x=-1
Therefore,
x = 5/7 or x=-1
D = b² - 4ac
D = 2² - 4(7)(-5)
D = 4 + 140
D = 144
D is positive, therefore, the equation has two distinct real roots.
Now,
x = [-b ± sqrt(D)] / 2a
x = [-2 ± sqrt(144)]/2×7
x =( - 2 ± 12) /14
x = (-2 + 12) /14 or x=(-2-12)/14
x = 10/14 or x= - 14/14
x = 5/7 or x=-1
Therefore,
x = 5/7 or x=-1
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