Find the discriminant of 5√2x²+8x-3√2=0
Answers
Answer:
The discriminant of an equation tells the nature of the roots of a quadratic equation given that a,b and c are rational numbers.
D=124
Step-by-step explanation:
Explanation:
The discriminant of a quadratic equation
ax2+bx+c=0
is given by the formula
b2+4ac of the quadratic formula;
x=−b±√b2−4ac
2a
The discriminant actually tells you the nature of the roots of a quadratic equation or in other words, the number of x-intercepts, associated with a quadratic equation.
Now we have an equation;
5
x
2
−
8
x
−
3
=
0
Now compare the above equation with quadratic equation
a
x
2
+
b
x
+
c
=
0
, we get
a
=
5
,
b
=
−
8
and
c
=
−
3
.
Hence the discriminant (D) is given by;
D
=
b
2
−
4
a
c
⇒
D
=
(
−
8
)
2
−
4
⋅
5
⋅
(
−
3
)
⇒
D
=
64
−
(
−
60
)
⇒
D
=
64
+
60
=
124
Therefore the discriminant of a given equation is 124.
Here the discriminant is greater than 0 i.e.
b
2
−
4
a
c
>
0
, hence there are two real roots.
Answer:
(8)^2-5(5√2) (2√2)=64-64=0