x² + $3 \sqrt{2}$ x – 8 = 0.

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Solution

Given: x² + $3 \sqrt{2}$ x – 8 = 0.
To find the nature of the roots, first we need to find the discriminant of the given quadratic equation.
We know that the discriminant of a quadratic equation is Δ = b² – 4ac.
On comparing the given equation with ay² + by + c = 0 in variable y, we get:
a = 1, b = $3 \sqrt{2}$ and c = –8
Thus,
Δ = ( $3 \sqrt{2}$ )² – 4(1)(–8)
=> Δ = 18 + 32 = 50
Since Δ > 0, the roots of the given quadratic equation are real and unequal.

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x2 + 32x – 8 = 0.

x² + $3 \sqrt{2}$ x – 8 = 0.