5+8x2= -5x find its nature of root
Answers
Answer:
Solution:-
Equation:-
\rm \: 8 {x}^{2} + 2x - 3 = 08x
2
+2x−3=0
Compare with
\rm \: a {x}^{2} + bx + c = 0ax
2
+bx+c=0
We get
\rm \: a = 8 \: \: \: \: b = 2 \: \: \: and \: \: \: c \: = - 3a=8b=2andc=−3
Find Discriminant
\rm \: D = {b}^{2} - 4acD=b
2
−4ac
\rm \: D = (2) {}^{2} - 4 \times 8 \times - 3D=(2)
2
−4×8×−3
\rm \: D = 4 + 96D=4+96
\rm \: D = 100D=100
D > 0 so, Nature of root is Real , Distinct
So using quadratic formula
\boxed{ \bf \: x = \frac{ - b \pm \sqrt{D} }{2a} }
x=
2a
−b±
D
put the value on quadratic formula
\rm \: x = \frac{ - 2 \pm \: \sqrt{100} }{2 \times 8}x=
2×8
−2±
100
\rm \: x = \frac{ - 2 \pm10}{16}x=
16
−2±10
\rm \: x = \frac{ - 2 + 10}{16} \: \: and \: \: \frac{ - 2 - 10}{16}x=
16
−2+10
and
16
−2−10
\rm \: x = \frac{8}{16} \: \: and \: \: \frac{ - 12}{16}x=
16
8
and
16
−12
Answer
\rm \: x = \frac{1}{2} \: \: and \: \: \frac{ - 3}{4}x=
2
1
and
4
−3
Step-by-step explanation:
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Answer:
Imaginary roots
Step-by-step explanation:
8x²+5x+5
now b²-4ac = 5²- 4(8x5)
= 25 - 160
= -135
Therefore the roots are imaginary
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