Question

Question 32 If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.

Class X1 - Maths -Sequences and Series Page 193

Answer 1

Let the root of quadratic equation are α and β
Then,
$AM = \frac{\alpha+\beta}{2}=8\\\\GM=\sqrt{\alpha.\beta}=5$$AM = \frac{\alpha+\beta}{2}=8\\\\GM=\sqrt{\alpha.\beta}=5$
hence,
α + β = 16 and , αβ = 25
now, we know,
a/c to quadratic equation:
the quadratic equation : x² -(sum of root)x + (product of root)
= x² -16x + 25
Hence, x² - 16x + 25 = 0

Answer 2

Answer is x^2-16x+25=0