Given: p(x) = 2x⁴ + 7x³ - 19x²- 14x + 30

Since x = √2 & - √2 is a solution so

x- √2 & x + √2 are two factors of p(x)

Multiplying the two factors we get x²-2 …Equation 1

which is also a factor of p(x)

To get the other two factors we need to perform long division

On performing long division we will get

2x² + 7x -15 …Equation 2

Equation 2 is also a factor of p(x)

To find the other two zeroes of the polynomial we need to solve Equation 2

We use the method of factorization for solving Equation 2

2x² + 7x -15 = 0

⇒ 2x² + 10x -3x -15 = 0

⇒ 2x(x + 5) -3(x + 5) = 0

⇒ (2x-3)(x + 5) = 0

The two roots are and -5