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The sum of all possible values of p for which atleast one root of equation x 4 – 8 x 3 + 22 x 2 – 24 x + p = 0 is of multiplicity 2, is

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one year ago

```							Dear student Roots are muliple of 2 Put 2 in the equation , 16 – 64 + 88 – 96 + p = 0 p = 56 Put x = 4 p = 0 Put x =8 p = – 1216 Dear student , There is no patern observed , Please attach image of the question , We will help you Good Luck
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one year ago
```							once again vikas ans is wrong as he doesnt even understand the meaning of multiplicity. note that for a root q to have multiplicity of 2, (x – q)^2 should be a factor of the given polynomial.let p(x)= x4 – 8x3 + 22x2 – 24x + p = 0then x4 – 8x3 + 22x2 – 24x + p = (x – q)^2*g(x)differentiate both sidesp’(x)= 4x^3 – 24x^2 + 44x – 24= 2(x – q)*g(x) + (x – q)^2*g’(x)= (x – q)*f(x) where f(x)= 2g(x) + (x – q)*g’(x) is a polynomial.so, clearly x= q is a root of p’(x).now, the roots of 4x^3 – 24x^2 + 44x – 24 are x= 1, 2, 3. so, q= 1, 2 or 3 should also be the root of p(x).when q=1, p(1)= – 9+p= 0 or p= 9when q=2, p(2)= – 8 + p= 0 or p= 8when q=3, p(3)= – 9+p= 0 or p= 9so, p= 8, 9so, sum of values of p is 8+9= 17kindly approve :)
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one year ago
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