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`        if α and β are the roots of  ax²+bx+c=0, then find roots of  a(x-2)²-b(x-2)(x-3)+c(x-3)²=0,`
3 months ago

```							Put alpha in ax^2+bx+c=0,it becomes a(alpha)^2+b(alpha)+c=0[as alpha is given as root of this equation]. Eq1From a(x-2)^2 + b(x-2)(x-3) +c(x-3)^2=0Take (x-3)^2 as common,it becomesa{(x-2)/(x-3)}^2+b{(x-2)/(x-3)} +c=0. Eq2Now compare the coefficient of a in Eq1 and Eq2We get aplha=x-2/x-3From here x=(3alpha-2)/alpha-1
```
3 months ago
```							Dear student Dear student ax^2 + bx(x-1) +c(x-1)^2 = 0ax^2 + bx^2 +bx + c^2 + c - 2cx =0x^2 (a-b+c) -x(2c -b) + c = 0 p+q = (2c -b)/a-b+cp.q = (c/a)/1-b/a+c/ap.q = alpha.Beta /(1-alpha + beta +alpha.beta)p+q = (alpha/alpha+1) + (beta/beta + 1)p.q = (alpha / alpha +1 ). (Beta/beta + 1)
```
3 months ago
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