find-the-number-of-values-of-p-for-which-equation-sin-3-x-1-p-3-3p-sin-x-0-p-gt-0-has-a-root- Tinku Tara June 4, 2023 Trigonometry 0 Comments FacebookTweetPin Question Number 158523 by gsk2684 last updated on 05/Nov/21 findthenumberofvaluesofpforwhichequationsin3x+1+p3−3psinx=0(p>0)hasaroot? Answered by mr W last updated on 05/Nov/21 lett=sinx−1⩽t⩽1t3−3pt+p3+1=0Δ=−p3+(p3+12)2=(p3−12)2⩾0forp3>1,i.e.p>1:t=p3−12−p3+123−p3−12+p3+123t=−1−p−1⩽−1−p⩽1−2⩽p⩽0≠p>1forp3<1,i.e.p<1:t=1−p32−p3+123−1−p32+p3+123t=−p−1−1⩽−p−1⩽1−2⩽p⩽0✓forp3=1,i.e.p=1:t3−3t+2=0t3−t2+t2−t−2t+2=0(t−1)2(t+2)=0⇒t=1✓,t=−2summary:−2⩽p⩽0orp=1forp>0thereisonlyonevaluep=1. Commented by gsk2684 last updated on 12/Nov/21 thankyousir(°⌣°) Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: n-2-n-n-2-n-Next Next post: find-the-differintial-equation-by-cancel-the-conestant-lny-ax-2-bx-c- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.