How do you solve the following with the quadratic formula?: sqrt2x² - x - 3sqrt(2) =0

2 Answers
Ratnaker Mehta
Jul 8, 2018

x=(3sqrt2)/2, or, x=-sqrt2.

Explanation:

Comparing the given quadratic equation with the standard one, i.e.,

ax^2+bx+c=0, we have,

a=sqrt2, b=-1, and c=-3sqrt2.

As per the quadratic formula, the roots are,

x={-a+-sqrtDelta}/(2a)," where, "Delta=(b^2-4ac).

In our case, Delta=(-1)^2-4(sqrt2)(-3sqrt2),

=1+24.

:. Delta=25," so that, "sqrtDelta=5.

Hence, -b+-sqrtDelta=1+-5=6, or, -4.

Finally, we get the roots : 6/(2sqrt2), or, -4/(2sqrt2),

i.e., 3/sqrt2=(3sqrt2)/2, or, -sqrt2.

Nam D.
Jul 8, 2018

x=-sqrt2,(3sqrt2)/2

Explanation:

Given: sqrt2x^2-x-3sqrt2=0.

Use the quadratic formula, which states that,

x=(-b+-sqrt(b^2-4ac))/(2a)

Here, a=sqrt2,b=-1,c=-3sqrt2.

:.x=(1+-sqrt(1-4*sqrt2*-3sqrt2))/(2sqrt2)

=(1+-sqrt(1+24))/(2sqrt2)

=(1+-sqrt25)/(2sqrt2)

=(1+-5)/(2sqrt2)

:.x_1=(1+5)/(2sqrt2)=6/(2sqrt2)=3/sqrt2=(3sqrt2)/2

:.x_2=(1-5)/(2sqrt2)=-4/(2sqrt2)=-2/sqrt2=-sqrt2

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