If X1, X2 are the roots of the quadratic equation ax? +bx+c = 0 and C+0, find the value of (ax, +b) ? +(ax, +b)? in terms of a, b, c. b р
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Given x 1 ,x 2 are the roots of ax
2 +bx+c=0⟹ax+b=− x
cax 1
+b=− x 1
c ,ax 2
+b=− x
2c⟹x 1 +x2
=− ab ,x1 x 2 = acx 12 +x 22 =(x 1 +x 2 ) 2 −2x 1 x 2a
b2 − a 2c = a 2b 2 −2ac
(ax +b) −2 +(ax
2 +b)
−2 =(− x 1c )
−2 +(− x 2c )
−2 =
c 2 x 12
+x 22
= a 2
c2 b 2−2ac
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