Question

If alpha, beta are the zeros of x²+ 7x +10, then alpha ,bata ==​

Answer 1

Answer:

x2 +5x+2x+10

x(x+5)+2(x+5)

(x+2)(x+5)

x= -2 or x= -5

Answer 2

x2+7x+10=0

(x+2)(x+5)=0

α,β=−2or−5

α3+β3=(−2)3+(−5)3=(−8)+(−125)=−133

The following alternate method can be used without actually calculating zeros. This method is especially useful when we have more complicated zeros.

For quadratic polynomial: ax2+bx+c

Sum of zeros =−ba

Product of zeros =ca

Quadratic polynomial x2+7x+10 has zeros α and β

α+β=−7

αβ=10

(α+β)3=(−7)3

α3+3α2β+3αβ2+β3=−343

α3+3αβ(α+β)+β3=−343

α3+3(10)(−7)+β3=−343

α3−210+β3=−343

α3+β3=−343+210

α3+β3= −133

Hence , bata = -133