10. Show that x2 + 2x + 7 has no real zeroes.
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x²+2x+7=0 is a quadratic equation as it's highest power is 2.
x²+2x+7=0
comparing the above equation with ax²+bx+c=0, we get ,
a=1,b=2,c=7
x=[-b±√(b²-4ac)]÷[2a]
..........(Formula)
x=[-2±√(2²-4×1×7)]÷[2×1]
= [-2±√(-24)]÷[2]
But -24 is not a real number.
Thus, x²+2x+7=0 has no real roots.
Thus, x²+2x+7=0 has no real zeroes.
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