How do you solve and write the following in interval notation: #x^2 + 6x + 5 >= 0#?

Answer 1

The interval notation is #] -oo,-5 ] uu [-1,+oo[#

Let's factorise the equation #y=x^2+6x+5>=0# #=>##(x+1)(x+5)>=0# Let's do a sign chart #color(white)(aaaa)##x##color(white)(aaa)##-oo##color(white)(aaaa)##-5##color(white)(aaa)##-1##color(white)(aaa)###+oo #color(white)(aa)##x+5##color(white)(aaaaaaa)##-##color(white)(aaa)##+##color(white)(aaa)##+##color(white)(aaa)# #color(white)(aa)##x+1##color(white)(aaaaaaa)##-##color(white)(aaa)##-##color(white)(aaa)##+##color(white)(aaa)# #color(white)(aaaaa)##y##color(white)(aaaaaaa)##+##color(white)(aaa)##-##color(white)(aaa)##+##color(white)(aaa)#
So #y>=0# on the intervals # ] -oo,-5 ] uu [-1,+oo[# graph{x^2+6x+5 [-10.8, 5.004, -5.31, 2.59]}
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Answer 2

To solve the inequality (x^2 + 6x + 5 \geq 0), first find the roots of the quadratic equation (x^2 + 6x + 5 = 0). The roots are (x = -1) and (x = -5). These are the points where the quadratic equation intersects the x-axis.

Plotting these points on a number line and testing points in each interval will determine the sign of the quadratic expression in that interval. This helps to determine the intervals where the inequality is satisfied (the quadratic expression is greater than or equal to zero).

The solution in interval notation is ([-5, \infty)).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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