Question

3x^2+2√5x-5 = 0 solve this equation by only prime factoraisation method

Answer 1

Answer:

$3x^2+2\sqrt{5}x-5=0$ can be factorized as $(x+\sqrt{5})(x-\sqrt{5})=0$.

Step-by-step explanation:

Consider the given quadratic equation,

$3x^2+2\sqrt{5}x-5=0$

Using prime factorization method,

Splitting middle term $2\sqrt{5}x$ as  $3\sqrt{5}x$ and $-\sqrt{5}x$ we get,

$3x^2+2\sqrt{5}x-5=0$ as,

$3x^2+3\sqrt{5}x-\sqrt{5}x-5=0$

taking 3x common from first two terms and $-\sqrt{5}$ common from next two terms, we get

$3x(x+\sqrt{5})-\sqrt{5}(x+\sqrt{5})=0$

$(x+\sqrt{5})(x-\sqrt{5})=0$

Thus, $3x^2+2\sqrt{5}x-5=0$ can be factorized as $(x+\sqrt{5})(x-\sqrt{5})=0$.