Question

for the quadratic equation x²-13x + 30 =0 alpha-beta =7 find alpha and beta​

Answer 1

Solution :

A quadratic equation is given as x² - 13x + 30 = 0

Now we'll find α + β

We know that formula for finding α + β is - coefficient of x/coefficient of x²

Here, coefficient of x is -13 and coefficient of x² is 1

So, α + β = -(-13)/1

α + β = 13 ...i)

α - β = 7 ...ii)

Now, add i) and ii)

=> α +β + (α - β) = 13 + 7

=> α + α = 13 + 7

=> 2α = 20

=> α = 20/2

=> α = 10

Now, put the value of α in i)

=> α + β = 13

=> 10 + β = 13

=> β = 13 - 10

=> β = 3

∴ Hence, α = 10 and β = 3 respectively.