Question

9. Determine the discriminant of 2x² - 6x + 7 = 0 and then state how many solutions there are; additionally,
state the nature of the solutions. Do not solve.

Answer 1

We need to find the nature of the roots of the quadratic equation 2x² - 6x + 7 = 0 , and need to find the Discriminant

Now ,as we know that the Discriminant of any quadratic equation of the form ax² + bx + c = 0 , is D = b² - 4ac

So now ;

${:\implies \quad \sf D=(-6)^{2}-4\times 2\times 7}$

${:\implies \quad \sf D=36-56}$

${:\implies \quad \bf \therefore \quad \underline{\underline{Discriminant=-20}}}$

Now , as D < 0 ,So nature of roots will be imaginary