Question

factorise
${x}^{2} + 3 \sqrt{2x} + 4$
​

Answer 1

Question:

Factorize the given polynomial ;

x² + 3√2x + 4 .

Answer:

(x + √2)(x + 2√2)

Zeros : x = -√2 , -2√2

Solution:

We have ;

=> x² + 3√2x + 4

=> x² + √2x + 2√2x + 4

=> x(x + √2) + 2√2(x + √2)

=> (x + √2)(x + 2√2)

Hence,

The factorized polynomial is ;

(x + √2)(x + 2√2)

Moreover,

If x² + 3√2x + 4 = 0

=> (x + √2)(x + 2√2) = 0

=> x = -√2 , - 2√2

Hence,

The zeros of the given quadratic polynomial are ; x = -√2 , -2√2

Answer 2

Given,

=x²+3√2x+4

=x²+√2x+2√2x+4

=x²+√2x+2√2x+2×√2×√2

=x(x+√2)+2√2(x+√2)

=(x+√2)(x+2√2)

x=-√2 OR x=-2√2

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