Q. 114.6( 18 Votes )

Determine if the equation has real roots and if so, find the roots.

Answer :

Given: The equation ,


To find: The roots if real.


Formula Used:


For a quadratic equation, ax2 + bx + c = 0,


D = b2 – 4ac


If D < 0, roots are not real


If D > 0, roots are real and unequal


If D = 0, roots are real and equal


The quadratic formula for finding the roots of quadratic equation
ax2 + bx + c = 0, a ≠ 0 is given by,



Explanation:


Consider,


Here a= √2, b = 7, c = 5√2


D = b2 – 4ac


D = 49 – (4 × 5√2 × √2)


= 49 – (20 × 2)


= 49 - 40


= 9 > 0


By quadratic formula,







Hence the roots are .


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