Home
Class 12
MATHS
If the quadratic equation a x^2+b x+6=0 ...

If the quadratic equation `a x^2+b x+6=0` does not have real roots and `b in R^+` , then prove that `a > m a x{(b^2)/(24),b-6}`

Text Solution

Verified by Experts

For the equation `ax^(2) + bx + 6 = 0` , roots are not real. Hence,
` D lt 0 rArr b^(2) - 24 a lt 0 or a gt (b^(2))/(24)`
Also, `f(0) = 6 gt 0 `. So ,
` f (-1) gt 0 rArr a + b + 6 gt 0`
`rArr a gt max {(b^(2))/(24), b -6}`.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.13|9 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise Single Correct Answer Type : Exercise|89 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.11|8 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

The quadratic equation x^(2)-2x+1=0 have no real root.

If a x^2+b x+6=0 does not have distinct real roots, then find the least value of 3a+bdot

If the roots of the quadratic equation x^(2)-m(2x-5)-6=0 are equal, then m=

If the roots of the quadratic equation (b-c)x^(2)+(c-a)x+(a-b)=0 are real and equal then prove that 2b=a+c.

If the sum of the roots of the quadratic equation a x^2+b x+c=0 is equal to the sum of the squares of their reciprocals, then prove that a/c , b/a a n d c/b are in H.P.

If he equation x^3+a x^2+b x+216=0 has three real roots in G.P., then b//a has the value equal to _____.

If the quadratic equations x^2+ax+b=0 and x^2+bx+a=0(aneb) have a common root , find the numerical value of (a+b).

Prove that the quadratic equation 2(a^(2)+b^(2))x^(2)+2(a+b)x+1=0 will have no real root if aneb .

If the roots of the quadratic equation (b-c)x^2+(c-a)x+(a-b)= 0 are equal, then prove that 2b=a+c.

If one of the roots of the quadratic equation be x^2 - (1+b)x+6 = 0 be 2, then find the other root.