Okay, so I suppose you know the quadratic formula from GCSE:
x=2a−b±b2−4ac.
Now, the number inside the square root determines whether or not a quadratic has real solutions, since if the expression inside the square root is negative, then the square root will give a complex number.
We call the bit inside the square root, ie b2−4ac the discriminant.
Can you work out what inequality the discriminant must satisfy for non-real roots, and hence answer the question?
Okay, so I suppose you know the quadratic formula from GCSE:
x=2a−b±b2−4ac.
Now, the number inside the square root determines whether or not a quadratic has real solutions, since if the expression inside the square root is negative, then the square root will give a complex number.
We call the bit inside the square root, ie b2−4ac the discriminant.
Can you work out what inequality the discriminant must satisfy for non-real roots, and hence answer the question?
b^2 has to be less than 44 to obtain a non-real complex number?
b^2 has to be less than 44 to obtain a non-real complex number?
Yes, so what range must b lie between?
(Hint: sketch the parabola y=x2 and look for the range of values where the curve lies below the line y=44. This will be a common technique for solving quadratic inequalities in A-level maths /FM)
(Hint: sketch the parabola y=x2 and look for the range of values where the curve lies below the line y=44. This will be a common technique for solving quadratic inequalities in A-level maths /FM)