Question

What is the nature the roots of quadratic equation 4x²-8x+9=0?​

Answer 1

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Quadratic Formula 4x^2-8x-9=0

4x2−8x−9=0

Use the quadratic formula to find the solutions.

−b±√b2−4(ac)/2a

Substitute the values

a=4

, b=−8

, and

c=−9

into the quadratic formula and solve for

x.8±√(−8)2−4⋅(4⋅−9)/2⋅4

Simplify.

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x=2±√13/2

The result can be shown in multiple forms.

Exact Form:

x=2±√13/2

Decimal Form:

x=2.80277563…,−0.80277563…

Answer 2

Comparing the given polynomial with ax²+bx+c=0

a=4, b=-8 and c=9

D = b²-4ac

D = (-8)²-4(4)(9)

D =64-144

D = -80

D <0

Therefore, Quadratic equation has no real roots.

Note:

A quadratic equation ax²+bx+c=0 has

(i) two distinct real roots, if D>0,

(ii) two equal roots,if D=0 and

(iii) no real roots,if D<0