Question

4) Use the discriminant formula to find the number of x-intercepts in the graph of the equation. 2x² + 4x + 2 = y a= b= C= Number of x-intercepts= b² - 4ac All cha​

Answer 1

Given :-

• A quadratic equation 2x² + 4x + 2 = 0 .

To find:-

• The number of x intercepts using the discriminant.

Answer:-

As we know that for a quadratic equation in standard form of ax² + bx+ c , discriminant is given by;

`\implies D = b^2 - 4ac`

with respect to standard form,

• a = 2
• b = 4
• c = 2

Aslo as we know that, when

• D = 0 , two equal roots , graph will touch x axis at single point .
• D > 0 , real roots , graph will cut x axis at two points .
• D < 0 , imaginary roots, graph will not cut the x axis .

So , we have ;

`\implies D = 4^2 - 4(2)(2)`

`\implies D = 16 - 16 =\boxed{0}`

Hence from the above mentioned points , the graph will cut x axis at single point . So will have only one x intercept .

And we are done!