Kindly help me with example 8 thanks

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# Question

# Answer

I see you have already gotten the answer on your paper.

Firstly, you know that:

**b**^{2}** – 4ac > 0**

If the discriminant is greater than zero, this means that the quadratic equation has **two real, distinct** (different) **roots.**

m(x^{2} – 3x + 2 ) = x^{2} -4x + 4

mx^{2 } -3mx + 2m = x^{2} -4x + 4

(m-1)x^{2} -(3m-4)x + (2m-4) = 0

**b**^{2}** – 4ac > 0 for 2 real and distinct roots**

**=> **[-(3m-4)]^{2 } – 4(m-1)(2m-4) > 0

9m^{2} -24m + 16 – 4(2m^{2} – 6m + 4) > 0

9m^{2} -24m + 16 – 8m^{2} + 24m – 16 > 0

m^{2} > 0 => m is non-zero and real numbers(includes rational and irrational, positive and negative, see the above chart for a comprehensive definition of real numbers)

I see you have already gotten the answer on your paper.

Firstly, you know that:

**b**^{2}** – 4ac > 0**

If the discriminant is greater than zero, this means that the quadratic equation has **two real, distinct** (different) **roots.**

m(x^{2} – 3x + 2 ) = x^{2} -4x + 4

mx^{2 } -3mx + 2m = x^{2} -4x + 4

(m-1)x^{2} -(3m-4)x + (2m-4) = 0

**b**^{2}** – 4ac > 0 for 2 real and distinct roots**

**=> **[-(3m-4)]^{2 } – 4(m-1)(2m-4) > 0

9m^{2} -24m + 16 – 4(2m^{2} – 6m + 4) > 0

9m^{2} -24m + 16 – 8m^{2} + 24m – 16 > 0

m^{2} > 0 => m is non-zero and real numbers(includes rational and irrational, positive and negative, see the above chart for a comprehensive definition of real numbers)

Thanks for your help as i am not sure whether my explanation is correct.

Could you please click on “Accept Answer”?

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