If a,b,c € R, a not equals to 0 and the quadratic

Question

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

Aditya Gupta · Accepted Answer

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+cso 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.

Differential Calculus> If a,b,c € R, a not equals to 0 and the q...

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 , 6 Years ago

Aditya Gupta

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differential calculus

Differential Calculus> If a,b,c € R, a not equals to 0 and the q...

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 , 6 Years ago

Aditya Gupta

LIVE ONLINE CLASSES

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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

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