How to use the discriminant to find out how many real number roots an equation has for $8b^2 - 6b + 3 = 5b^2$ ?

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Answer 1 · 2018-04-16T01:44:31

$color(crimson)("The given equation has TWO REAL ROOTS"$

For a given quadratic equation in the standard form $ax^2 + bx + c$ ,

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$"Discriminant " D = b^2 - 4ac$

$8b^2 - 6b + 3 = 5b^2$

$8b^2 - 5b^2 - 6b + 3 = 0, " making R H S = 0"$

$3b^2 - 6b + 3 = 0$

$:. D = b^2 - 4 a c = (-6)^2 - (4 * 3 * 3) = 36 - 24 = 12, color(green)(" which is " > 0 " (Positive)"$

Hence $color(crimson)("The given equation has TWO REAL ROOTS"$

How to use the discriminant to find out how many real number roots an equation has for 8b^2 - 6b + 3 = 5b^28b^2 - 6b + 3 = 5b^2?