Text Solution Solution : Given `p(x)=2x^4+7x^3−19x^2−14x+30`<br> Two of its zeroes are `sqrt(2) `and `−sqrt(2)`<br> so,`g(x)=(x−sqrt(2))(x+sqrt(2))`<br> or,`x^2−2`<br> so we get <br>,divisor=`x^2−2`<br> Quotient=`2x^2+7x−15`<br> Remainder=`0`<br> so,`q(x)=−2x^2+7x−15`<br> `2x^2+10x−3x−15=0`<br> =`2x(x+5)−3(x+5)=0`<br> =`(2x−3)(x+5)=0`<br> thus,`x=3/2,-5`<br>so,roots of equation is `sqrt(2) ,−sqrt(2) ,3/2 ` and `−5`
Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also, verify the relationship between the zeroes and coefficients in each case: Let p(x) = 2x3+x2–5x + 2 Comparing the given polynomial with ax3 + bx3 + cx + d, we get Now,
and ∴ are the zeroes of Hence, verified.Here, we have Now, and Hence verified. |