If a,b,c € R, a not equals to 0 and the quadratic equation,ax2 + bx + C = 0 has no real root, then show that a(a+b+c)>0

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Grade 12Differential Calculus

If a,b,c € R, a not equals to 0 and the quadratic equation,ax²+ bx + C = 0 has no real root, then show that a(a+b+c)>0

Alka Sinha

7 Years agoGrade 12

1 Answer

Aditya Gupta

7 Years ago

this is an easy ques based on graph of a quadratic function.

assume that a is positive.

then the graph of y= f(x)= ax²+ bx + c would be above the x axis since it has no real root.

so f(1) is greater than zero.

but f(1)= a+b+c

so a+b+c is greater than zero.

so a(a+b+c) is greater than zero.

now assume that a is less than zero.

then the graph of y= f(x)= ax²+ bx + c would be below the x axis since it has no real root.

so f(1) is less than zero.

so a+b+c is less than zero.

so a(a+b+c) is greater than zero.

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If a,b,c € R, a not equals to 0 and the quadratic equation,ax2 + bx + C = 0 has no real root, then show that a(a+b+c)>0

Alka Sinha

1 Answer

Aditya Gupta

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